Class 9

MP Board Class 9th Maths Solutions Chapter 13 Surface Areas and Volumes Ex 13.6

Assume = \(\frac{22}{7}\) unless stated otherwise.

Question 1.
The circumference of the base of a cylindrical vessel is 132 cm and its height is 25 cm. How many litres of water can it hold? (1000 cm³ = 1l)
Solution:
Circumference of base, C =132 cm ,
h = 25 cm
C = 2πr
132 = 2 x \(\frac{22}{7}\) x r
r = \(\frac{132×7}{2×22}\) = 21 cm
Volume of cylinder =πr²h
= \(\frac{22}{7}\) x 21 x 21 x 25 = 34650 cm³
= \(\frac{34650}{1000}\)

Question 2.
The inner diameter of a cylindrical wooden pipe is 24 cm and its outer diameter is 28 cm. The length of the pipe is 35 cm. Find the mass of the pipe, if 1 cm3 of wood has a mass of 0.6 g.
Solution:

Inner diameter
d₁ = 24 cm ⇒ r₁ = 12 cm
Outer diameter, d₂ = 28 cm ⇒ r₂ = 14 cm
Volume of wood in the piple = πr₂²h – πr₁²h
πh(r₂² – r₁²) = \(\frac{22}{7}\) x 35(14² – 12²)
= \(\frac{22}{7}\) x 35 x 52 = 5720 cm³
Mass of pipe = 0.6 x 5720 = 3432 gm
= 3.432 kg.

Question 3.
A soft drink is available in two packs –

1. a tin can with a rectangular base of length 5 cm and width 4 cm, having a height of 15 cm and
2. a plastic cylinder with circular base of diameter 7 cm and height 10 cm. Which container has greater capacity and by how much?

Solution:
1. Volume of cuboidal can = (5 x 4 x 15) = 300 cm³

2. Volume of cylindrical can = πr²h = \(\frac{22}{7}\) x 3.5 x 3.5 x 10
= 385 cm²
Capacity of cylindrical can is more than the cuboidal can by 85 cm2.

Question 4.
If the lateral surface of a cylinder is 94.2 cm2 and its height is 5 cm, then find

1. radius of its base
2. its volume. (Use π = 3.14)

Solution:
1. CSA of cylinder = 94.2 cm²
2πrh = 94.2 cm²
2 x 3.14 x 5 = 94.2 cm²
r = \(\frac{94.2}{2×3.14×5}\) = 3 cm
Volume of the cylinder = πr²h
= 3.14 x 3 x 3 x 5
= 3.14 x 45 = 141.3 cm³

Question 5.
It costs ₹ 2200 to paint the inner curved surface of a cylindrical vessel 10 m deep. If the cost of painting is at the rate of ₹ 20 per m², find

1. inner curved surface area of the vessel
2. radius of the base
3. Capacity of the Vessel.

1. Inner curved surface area =

2. Let r be the radius of the base ICSA = 2πrh
110 = 2 x \(\frac{22}{7}\) x r x 10 r
= 1.75 m

3. Capacity of vessel = πr²h = \(\frac{22}{7}\) x 1.75 x 1.75 x 10
= 96.25 m³.

Question 6.
The capacity of a closed cylindrical vessel of height 1 m is 15.4 litres. How many square metres of metal sheet would be needed to make it?
Solution:
h = 1 m
V = 15.4l
= \(\frac{15.4}{1000}\)m³ = 0.0154 m³
Volume of the vessel = πr²h
0. 0154 = \(\frac{22}{7}\) x r² x 1
∴ r² = \(\frac{0.0154×7}{22}\)
⇒ r² = 0.0049
∴ r = 0.07 m
Area of metal sheet required = 2nr (h + r)
= 2x \(\frac{22}{7}\) x 0.07(1 + 0.07)
= 0.4708 m².

Question 7.
A lead pencil consists of a cylinder ofvyood with a solid cylinder of graphite filled in the interior. The diameter of the pencil is 7 mm and the diameter of the graphite is 1 mm. If the length of the pencil is 14 cm, find the volume of the wood and that of the graphite.
Solution:
Volume of the pencil = πr²h
= \(\frac{22}{7}\) x 3.5 x 3.5 x 140 = 5390 mm³
Volume of graphite = πr²h
= \(\frac{22}{7}\) x 0.5 x 0.5 x 140 = 110 mm³
Volume of wood = Volume of pencil – Volume of graphite
= 5390 – 110
= 5280 mm³
=5.28 cm³.

Question 8.
A patient in a hospital is given soup daily in a cylindrical biftvl of diameter 7 cm. If the bowl is filled with/soup to a height of 4 cm, how much soup the hospital has to prepare daily to serve 250 patients?
Solution:
d = 7cm
r = 3.5 cm
h = 4cm
Volume of the bowl = πr²h
= \(\frac{22}{7}\) x 3.5 x 3.5 x 4 = 154 cm³
Volume of soup needed for 250 patients = 154 x 250
= 38500 cm³
= 38.5l.

MP Board Class 9th Maths Solutions

MP Board Class 9th General English Grammar Reporting

अंग्रेजी में किसी के कहे हुए वचन को दो प्रकार से प्रकट कर सकते हैं

(1) यदि किसी व्यक्ति के वही शब्द लिखे जाएँ जो उसने कहे हैं और उनमें किसी प्रकार की तब्दीली न की जाए तो उसे Direct Speech कहते हैं। जैसे

Rama said, “She is a good girl.”
यहाँ बोलने वाले के ठीक-ठीक वही शब्द दिए गए हैं।

Direct Speech
में निम्न बातों का ध्यान रखना चाहिए

(a) बोलने वाले के असली शब्दों को inverted commas (“…”) में लिखते हैं।
(b) बोलने वाले के असली शब्दों को Reported Speech कहते हैं।
(c) जो Verb (क्रिया) ‘Reported Speech’ के सम्बन्ध में कुछ बताता है उसे Reporting verb कहते हैं।

(2) जब हम बोलने वाले के असली शब्दों का प्रयोग नहीं करते परन्तु उनका तात्पर्य या अर्थ लिखते हैं तो उसे Indirect Speech कहते हैं जैसे
Rama said that she was a good girl.
Indirect speech में निम्न बातों का ध्यान रखना चाहिए

Rama said that she was a good girl.
Indirect speech में निम्न बातों का ध्यान रखना चाहिए

(a) इसमें कोई inverted commas नहीं होते। बोलने वाले के ठीक वही शब्द नहीं लिखे जाते। उनमें कुछ परिवर्तन किया जाता है।
(b) Reporting verb के बाद कोई comma नहीं लगाया जाता।
(c) Reported Speech À ved Conjunction that का प्रयोग होता है।
(d) Reported speech की क्रिया को बदलते हैं।
जब हम Direct speech को Indirect speech में बदलते हैं तो अग्रांकित बातों का ध्यान रखते हैं;

जैसे-

(1) Said को told में बदल देते हैं। Persons में परिवर्तन निम्न रूप में करते हैं।
I person के Pronoun (I, we, us, our) का परिवर्तन Direct Speech के Subject (कर्ता) के Person के अनुसार होता है II Person के Pronoun (You, Your) का परिवर्तन Object के अनुसार होता है तथ III Person के Pronoun (he, she, it, her) में कोई भी परिवर्तन नहीं होता है

(2) निकटता प्रकट करने वाले शब्दों में परिवर्तन निम्नलिखित रूप से किया जाता है-

• Now – then
• This – that
• Ago – before
• Tonight – that night
• Last night – the previous night
• Here – there
• these – those
• A year ago – a year before
• Today – that day
• Tomorrow – the next day
• Yesterday – the day before
• Just – then
• Come here – go there
• Next week – the following week

(3) Tense (काल) परिवर्तन-
(a) Reporting Verb के Present या Future Tense में होने पर Reported verb के Tense में कोई परिवर्तन नहीं होता।

(b) Reporting verb के Past Tense में होने पर Reported Verb के Tense में परिवर्तन होता है-

(i) Simple Present का Simple Past हो जाता है।
He said, “She works hard.”
He said that she worked hard.

(ii) Present Continuous का Past Continuous हो जाता है जैसे-
He said, “She is reading a book.”
He said that she was reading a book.

(iii) Present Perfect का Past Perfect हो जाता है

जैसे-
Hema said, “Ram has done his work”.
Hema said that Ram had done his work.

(iv) Present Perfect Continuous का Past Perfect Continuous हो जाता है जैसे-
Shyam said, “Ram has been working for two hours.”
Shyam said that Ram had been working for two hours.

(v) Simple Past का Past Perfect हो जाता है।

जैसे-
Sita said, “Rita read a book.”
Sita said that Rita had read a book.

(vi) Past Continuous का Past Perfect Continuous हो जाता है।

जैसे-
“Gopal said, “Govind was singing a song.”
Gopal said that Govind had been singing a song.

Shall का should, may का might, can का could हो जाता है तथ सदा सत्य व् ऐतिहासिक ताद्यों का नहीं बदलता

(1) Interrogative Sentences
Direct-Rahul said to Rama, “Is it easy to ride a bicycle ?”
Indirect-Rahul asked Rama if it was easy to ride a bicycle.
Direct—The bird said to the Prince, “Why are you weeping?”
Indirect—The bird asked the Prince why he was weeping.

Commands and Orders
Direct—Father said, “Get some milk.”
Indirect—Father told him to get some milk.
Direct—Hari said to me, “Please help me.”
Indirect—Hari requested me to help him.

Statements…

Exercise-1

Change into indirect speech.
1. Hari Babu said, “This porter carries the luggage with great care.”
2. The doctor said, “The patient does not take medicine.”
3. He said, “The man has been talking for a long time.”
4. She said, “I am drawing a picture.”
5. Pratap said, “I have fought a long battle.”
6. You said to me, “I gave you my pen.”
7. You said, “I was not saving money.”
Answer:
1. Hari Babu said that that porter carried the luggage with great care.
2. The doctor said, that the patient did not take medicine.
3. He said that the man had been talking for a long time.
4. She said that she was drawing a picture.
5. Pratap said that he had fought a long battle.
6. You told me that you had given me your pen.
7. You said that you had not been saving money.

(2) Interrogative Sentences

Exercise-2

Change into indirect speech.
1. My father said to me, “Are you going to Kanpur today?”
2. He said to me, “Do you go to cinema very often ?”
3. His brother said to me, “Was Gopal sitting on the bench ?”
4. Mr. Gupta said to me, “Will you take me too with you ?”
5. The guest said to the boy, “Did you see this film ?”
Answer:
1. My father asked me if I was going to Kanpur that day.
2. He asked me if I went to cinema often.
3. His brother asked me whether Gopal had been sitting on the bench.
4. Mr. Gupta asked me if I would take him too with me.
5. The guest asked the boy whether he had seen that film.

(3) Imperative Sentences (Commands and Requests)

Exercise-3
Change into indirect speech.
1. The old man said to the boy, “Get out of the room.”
2. He said to me, “Please do it first.”
3. I said to him, “Don’t open the box.”
4. The clergyman said to him, “May God recover you soon.”
5. She said to me, “How clever you are !”
6. The actor said, “What a beautiful scene it is !”
7. They said, “Alas ! Our beloved leader is departed !”
Answer:
1. The old man ordered the boy to get out of the room.
2. He requested me to do it first.
3. I asked him not to open the box.
4. The clergyman wished that God might recover him soon… !
5. She exclaimed with admiration that I am very clever.
6. The actor exclaimed with joy that the scene was very beautiful.
7. They exclaimed with grief that their beloved leader was departed.

MP Board Class 9th English Solutions

MP Board Class 9th Maths Solutions Chapter 13 Surface Areas and Volumes Ex 13.4

Assume π = \(\frac{22}{7}\), unless stated otherwise.

Question 1.
Find the surface area of a sphere of radius:

(i) 10.5 cm
(ii) 5.6 cm
(iii) 14 cm

Solution:
(i) Here r = 10.5 cm
∴ Surface area of the sphere = 4πr²

Question 2.
Find the surface area of a sphere of diameter:

(i) 14 cm
(ii) 21 cm
(Hi) 3.5 m

Solution:
(i) Here, Diameter = 14 cm

Question 3.
Find the total surface area of a hemisphere of radius 10 cm. (Use π = 3.14)
Solution:
Here, radius (r) = 10 cm

Question 4.
The radius of a spherical balloon increases from 7 cm to 14 cm as air is being pumped into it. Find the ratio of surface areas of the balloon in the two cases.
Solution:
Initial radius of the balloon, r₁ = 7 cm
Final radius of the balloon, r₂ = 14 cm
Initial surface area of the balloon = S₁
Final surfacg area of the balloon = S₂

S₁ : S₂ = 1 : 4

Question 5.
A hemispherical bowl made of brass has inner diameter 10.5 cm. Find the cost of tin-plating it on the inside at the rate of ₹ 16 per 100 cm².
Solution:
d = 10.5 cm
r =5.25 cm
Rate of tinplating = \(\frac{16}{100}\) = ₹ 0.16 per cm²
Inner curved surface area of bow l = 2 πr²
ICSA = 2 x \(\frac{22}{7}\) x 5.25 x 5.25 = 173.25 cm²
Cost of tin-plating = Rate x ICSA
= 0.16 x 173.25 = ₹ 27.72

Question 6.
Find the radius of a sphere whose surface area is 154 cm².
Solution:
Surface area of sphere = 4 πr2
154 = 4 x \(\frac{22}{7}\) x r²
\(\frac{154×7}{4×22}\) = r²
⇒ r² = 3.5 cm.

Question 7.
The diameter of the moon is approximately one-fourth of the diameter of the earth – Find the ratio of their surface areas.
Solution:
d₁ = \(\frac{1}{4}\)d₂

Let .S₁, and .S₂, be the surface area of moon and earth respectively.
S₁ = 4 πr₁²
S₂ = 4 πr₂²

Question 8.
A hemispherical bowl is made of steel, 0.25 cm thick. The inner radius of the bowl is 5 cm. Find the outer curved surface area of the bowl.
Solution:
r₁ = 5 cm
t (thickness) = 0.25 cm
r₂ = r₁ + t
= 5 + 0.25 = 5.25 cm
OCSA of bowl = 2x \(\frac{22}{7}\) x 5.25 x 5.25
= \(\frac{44}{7}\) x 5.25 x 5.25 = 173.25 cm²

Question 9.
A right circular cylinder just encloses a sphere of radius r (see Fig.). Find

1. surface area of the sphere.
2. curved surface area of the cylinder.
3. ratio of the areas obtained in (i) and (ii).

Solution:
As the sphere just encloses a right circular cylinder, the height of the cylinder is equal to the diameter of the sphere.
∴ Height of cylinder h = 2r
where r is the radius of sphere

1. Surface area of sphere S₁ = 4πr²

2. CSA of a cylinder,= 2πrh
= 2πr x 2r = 4πr²

3.

MP Board Class 9th Maths Solutions

MP Board Class 9th General English Grammar Passive Voice

अंग्रेजी भाषा में दो प्रकार की voice होती हैंActive and Passive Voice

We drink milk. (Active voice)
हम दूध पीते हैं।

Milk is drunk by us.” (Passive voice)
दूध हमारे द्वारा पिया जाता है।

मुख्य बातें-
(1) केवल कर्म (object) वाले वाक्यों को Passive voice में बदला जा सकता है। बिना कर्म वाले वाक्यों को Passive voice में नहीं बदला जा सकता है।

जैसे-
He sleeps. Radha is weeping.
इन वाक्यों में object नहीं है इसलिए इन्हें Passive में नहीं बदला जा सकता है।

(2) Perfect Continuous वाक्यों को Passive वाक्यों में नहीं बदला जाता है

जैसे-
She has been waiting for me.

(3) Future Continuous वाक्यों को Passive वाक्यों में वाक्यों में नहीं बदला जाता है

जैसे
-I shall be going to Delhi.

(4) Passive Voice में Past participle (Third form of the verb) का प्रयोग होता है
I sing a song. (Active)
A song is sung by me.b (Passive)

Tenses Change of Voice
Continuous Tenses

(1) Present Continuous Tense Active Voice
Structure-Subject-am/is/are (not) verb + ing-object etc.
(i) Are they borrowing money?
(ii) His brother is earning a lot of money.

Passive Voice
(i) Is money being borrowed by them?
(ii) A lot of money is being earned by his brother?

Exercise-1

Change into Passive Voice :
[Structure-Object-am/is/are + being + verb III (other words) by subject]

1. Seema is cutting fruits.
2. The gardner is plucking dead leaves.
3. I am sending a parcel to Rohan.
4. The shopkeeper is selling rice.
5. Are they reading books?
Answer:
1. Fruits are being cut by Seema.
2. Dead leaves are being plucked by the gardener.
3. Rohan is being sent a parcel by me.
4. Rice is being sold by the shopkeeper.
5. Are books being read by them.

(2) Past Continuous Tense

Active Voice
Structure_Subject—was/were + verb + ing object etc. :

(i) He was singing a song.
(ii) She was not writing essays.
(iii) You were throwing balls.

Passive Voice
Structure-Object—was/were + being verb III form (other words by subject).

(i) A song was being sung by him.
(ii) Essays were not being written by her.
(iii) Balls were being thrown by you.

Exercise-2
Change into Passive Voice :
Structure-Object–was/were + being + verb III (other words) by subject.

1. His sister was knitting a sweater.
2.Why was she keeping plates into the Almirah?
3. I was learning Mathematics.
Answer:
1. A sweater was being knitted by his sister.
2. Why were plates being kept by her in the almirah?
3. Mathematics was being learnt by me.

(3) Future Continuous Tense
इस Tense की Passive Voice नहीं होती,यह सिर्फ Active Voice में ही लिखा जाता है

Indefinite Tenses

(1) Present Indefinite Tense

Active Voice
(i) You catch fish.
(ii) Sunita dries clothes.

Passive Voice
(i) Fish is caught by you.
(ii) Clothes are dried by Sunita.

Exercise-3

Change into Passive Voice :
Structure-am/is/are (not) verb III form… by subject.

1. We supply hardware material.
2. You sell standard goods.
3. She does not cut fruits.
4. Do you lend money?
5. Where do you send the parcels?
Answer:
1. Hardware material is supplied by us..
2. Standard goods are sold by you.
3. Fruits are not cut by her.
4. Is money lent by you?
5. Where are parcels sent by you?

(2) Past Indefinite Tense

Active Voice
(i) I broke the glass.
(ii) You knew me.

Passive Voice
(i) The glass was broken by me.
(ii) I was known to you.

Exercise-4

Change into Passive Voice : Structure-was/were + verb III by subject.

1. They did not bring pens.
2. Did she clean the rooms?
3. How many pens did she buy?
4. Ravi wrote a letter to Shyam.
Answer:
1. Pens were not brought by them.
2. Were rooms cleaned by her?
3. How many pens were brought by her?
4. A letter was written to Shyam by Ravi.

(3) Future Indefinite Tense

Active Voice
(i) We shall see the match.
(ii) The boys will play the match.

Passive Voice
(i) The match will be seen by us.
(ii) Match will be played by the boys.

Exercise-5

Change into Passive Voice :
1. Will you omit five questions?
2. My work will satisfy you.
3. Your brother will buy a clock.
4. My mother will look after you.
Answer:
1. Will five questions be omitted by you.
2. You will be satisfied with my work.
3. A clock will be bought by your brother.
4. You will be looked after by my mother.

Perfect Tenses
(1) Present Perfect Tense

Active Voice
(i) I have done the work.
(ii) She has spent the money.

Passive Voice
(i) The work has been done by me.
(ii) All the money has been spent by her.

Exercise-6

Change into Passive Voice :
Structure-has/have + been + verb III form by subject.

1. She has lost her purse.
2. The officer has signed the papers.
3. We have smelt the flowers.
4. You have paid the fees.
5. The students have prepared the essays.
Answer:
1. Her purse has been lost.
2. The papers have been signed by the officer.
3. The flowers have been smelt by us.
4. The fees has been paid by you.
5. The essays have been prepared by the students.

(2) Past Perfect Tense

Active Voice :
(i) Seema had drunk the tea.
(ii) The police had arrested the thief.

Passive Voice
(i) The tea had been drunk by Seema.
(ii) The thief had been arrested by the police.

Exercise-7

Change into Passive Voice :
StructureObject—had been + verb III form by subject.

1. The girls had collected the dresses.
2. They had not finished the work.
3. Had they invited us?
4. I had found my bag.
Answer:
1. The dresses had been collected by the girls.
2. The work had not been finished by them.
3. Had we been invited by them?
4. My bag had been found by me.

(3) Future Perfect Tense

Active Voice
(i) The girl will have taken tea.
(ii) She will have mentioned my name.

Passive Voice
(i) Tea will have been taken by the girl.
(ii) My name will have been mentioned by her.

Exercise-8

Change into Passive Voice :
Structure-Object—shall/will + have been verb III by subject.

1. He will have called me.
2. The guard will have blown the whistle.
3. You shall have done the work.
Answer:
1. I will have been called by him.
2. The whistle will have been blown by the guard.
3. The work shall have been done by you.

Imperative Sentences

Active Voice
(i) Buy some wool.
(ii) Do not think this.

Passive Voice
(i) Let some wool be bought.
(ii) Let this not be thought.

Exercise-9

Change into Passive Voice : Structure-Let + object + be + verb III form.
1. Forget all your sorrows.
2. Never tell lies.
3. Do not spend all the money.
Answer:
1. Let all your sorrows be forgotten.
2. Let lies never be told.
3. Let all the money not be spent.

Exercise-10

Change the following sentences into Passive Voice.
1. We killed a cobra.
2. Will you deliver the letters?
3. You please me.
4. The fisherman caught a fish.
5. Ram will speak the truth.
6. Sita kills a snake.
7. Hari did the work.
8. She is singing a song.
9. One should keep one’s promise.
10. Open the door.
Answer:
1. A cobra was killed by us.
2. Will the letters be delivered by you?
3. I am pleased with you.
4. A fish was caught by the fisherman.
5. The truth will be spoken by Ram.
6. A snake is killed by Sita.
7. The work was done by Hari.
8. A song is being sung by her.
9. One’s promise should be kept.
10. Let the door be opened.

MP Board Class 9th English Solutions

MP Board Class 9th General English Grammar Tenses

परिभाषा- The tense of a verb shows the time of an event or action of a verb.

Verb के tense से किसी घटना या कार्य के समय का ज्ञान होता है।

अंग्रेजी में Tense तीन प्रकार के होते हैं-
(i) Present tense
(ii) Past tense
(iii) Future tense.

(i) Present Tense (वर्तमान काल)—इस Tense से यह पता चलता है कि कार्य अब या अभी हुआ है। जैसे
I go to school.
(मैं स्कूल जाता हूँ।)

(ii) Past Tense (भूतकाल)—इस Tense से यह पता चलता है कि कार्य बीते हुए समय में हुआ है। जैसे
I went to school.
(मैं स्कूल गया।)

(iii) Future Tense (भविष्य काल)—इस Tense से यह पता चलता है कि कार्य आने वाले समय में होगा। जैसे
I shall go to school.
(मैं स्कूल जाऊँगा।)

प्रत्येक Tense निम्नलिखित चार प्रकार का होता है
1. Indefinite,
2. Continuous,
3. Perfect;
4. Perfect Continuous.

Present Tense (वर्तमान काल)
(1) Present Indefinite Tense-इस Tense में सदा सत्य बातें, आदतें अथवा बार-बार होने वाले कार्यों का वर्णन किया जाता है। जैसे

(i) The sun rises in the east.
सूर्य पूर्व में उदय होता है।

(ii) I go to school.
मैं स्कूल जाता हूँ।

पहचान-हिन्दी में वाक्यों के अन्त में ता, ती, ते तथा हैं, हूँ, हो होता है।
Structure -Subject + I form of verb + s, es, ies + object.

Like :
(i) Ram calls Mohan.
(ii) I eat guavas daily.

Exercise-1

Rewrite the following using correct form of the verb given in the brackets.
1. Shyam ………….. up at 6’0 clock. (get/gets)
2. They………. football in summers. (play/plays)
3. Geeta ……………. Physics from Mohan. (study/studies)
4. The sun …………….. in the east. (rise/rises)
5. One of you ………….. with me. (come/comes)
Answer:
1. gets,
2. play,
3. studies,
4. rises,
5. come.

Making the Verb Emphatic or Strong
इस tense में do या does सहायक क्रिया + I form of __verb से verb को emphatic या strong बनाया जाता है। अगर वाक्य में verb की I form है तो केवल do जोड़ा जाता है व verb की I form के साथ s, es, ies जुड़ा हो तो does जोड़कर verb में से s, es, ies हटा दिया जाता है।

Making Negative Emphatic Verb
Negative बनाने के लिए subject के बाद do not या does not + verb की I form प्रयोग करते हैं।

जैसे-
(i) I do not eat potatoes.
(ii) She does not speak French.

Exercise-2

Rewrite the following in negative form.
1. Sohan eats bananas.
2. Kamla goes to school.
3. We drink milk.
4. Mala dries clothes.
5. Each one of them works hard.
Answer:
1. Sohan does not eat bananas.
2. Kamla does not go to school.
3. We do not drink milk.
4. Mala does not dry clothes.
5. Each one of them does not work hard.

Making the Interrogative form—
Interrogative बनाने के लिये Do/Does का sentence के प्रारम्भ में प्रयोग करते हैं व अन्त में प्रश्नवाचक चिह्न लगाते हैं। जैसे-
(i) Do you play hockey?
(ii) Does she bring coffee?

Exercise-3

Rewrite the following sentences into interrogative.
1. She sings songs.
2. I speak the truth.
3. She calls her parents.
4. Sunita and Ram read well.
5. Cats drink milk.
Answer:
1. Does she sing songs?
2. Do I speak the truth?
3. Does she call her parents?
4. Do Sunita and Ram read well?
5. Do cats drink milk?

(2). Present Continuous Tense
इस Tense chat प्रयोग तब किया जाता है जब कार्य अभी भी चल रहा हो; जैसे
I am writing a letter.
मैं पत्र लिख रहा हूँ।

पहचान-हिन्दी में वाक्यों के अन्त में रहा हूँ, रहा है, रही है, रहे हैं होता है।

Structure—Subject + am/is/are Verb + ing + object etc. Negative ha fet am/is/are o are not STIRI GIAI. Subject + am/is/are + not verb + ing + object.

☆ Interrogative बनाने के लिए-
Am/Is/Are + Subject (not) verb + ing + object.

Exercise-1

Write the following sentences in Present Continuous Form. 1. You …….. the bicycle. (ride)
2. I ……. a pen. (buy)
3. She ……… a letter. (write)
4. They ……. T.V. (watch)
5. Anita ……… late for school. (get)
Answer:
1. are riding,
2. am buying,
3. is writing,
4. are watching,
5. is getting.

Exercise-2

Make the sentences negative.
1. She is cutting the vegetables.
2. Radha is going to the shop.
3. Meena is working hard for the examinations.
4. I am calling you.
Answer:
1. She is not cutting the vegetables.
2. Radha is not going to the shop.
3. Meena is not working hard for the examinations.
4. I am not calling you.

Exercise-3

Make following sentences interrogative.
1. He is not walking quickly.
2. Mala is writing carefully.
3. People in India are living peacefully.
Answer:
1. Is he not walking quickly?
2. Is Mala writing carefully?
3. Are people in India living peacefully?

(3) Present Perfect Tense-इस Tense of im ऐसे कार्य के लिए होता है जो वर्तमान में पूरा हो चुका है।
जैसे-
(i) I have done my work.
मैंने अपना काम कर लिया है।

(ii) He was written a letter.
वह एक पत्र लिख चुका है।

इसमें I, You तथा बहुवचन के साथ have तथ एकवचन के साथ has का प्रयोग किया जाता है इसमें verb की III form का ही प्रयोग होता है।

पहचान-हिन्दी में वाक्यों के अन्त में किया है, दिया है, चुका है, चुके हैं, चुका हूँ आदि होता है।

Structure-subject + has/have + verb III form | (past participle) + object

Negative बनाने के लिए have/has के बाद not का प्रयोग होता है।
Interrogative बनाने के लिए Have/Has को sentence के प्रारम्भ में subject से पूर्व प्रयोग किया जाता है।

Exercise-1

Fill in the blanks with the correct form of the verb.
1. I ……… the bell. (ring)
2. Seema ……… her work. (begin)
3. People ……… on him. (shout)
4. They ……… the shop. (close)
Answer:
1. have rung,
2. has begun,
3. have shouted,
4. have closed.

(4) Present Perfect Continuous Tense- इस Tense में कार्य पहले से हो रहा है तथा वर्तमान में भी जारी है। जैसे-

(i) I have been writing a letter for an hour.
मैं एक घण्टे से पत्र लिख रहा हूँ।

(ii) It has been raining since morning.
सुबह से वर्षा हो रही है।

इस Tense में subject के अनुसार has been या have been तथा मुख्य क्रिया में ing लगाते हैं। समय के लिए for या since का प्रयोग होता है।

Structure-subject + have been/has been + verb + ing + object-since/for time.

Exercise-1

Fill the following sentences in the Present Perfect Continuous Tense.
1. She ……… (write) a book ……… yesterday.
2. He ……… (play) the game ……… an hour.
3. The mob ……… (revolt) ……… years.
Answer:
1. has been writing, since,
2. has been playing, for,
3. has been revolting, since.

MP Board Class 9th English Solutions

MP Board Class 9th Maths Solutions Chapter 13 Surface Areas and Volumes Ex 13.3

Assume π = \(\frac{22}{7}\), unless stated otherwise.

Question 1.
Diameter of the base of a cone is 10.5 cm and its slant height is 10 cm. Find its curved surface area.
Solution:
Here, diameter of the base = 10.5 cm
Radius (r) = \(\frac{10.5}{2}\)
Slant height (l) = 10 cm
Curved surface area of the cone = πrl
= \(\frac{22}{7}\) x \(\frac{10.5}{2}\) x 10 cm²
= \(\frac{22}{7}\) x \(\frac{10.5}{20}\) x 10 cm²
= 11 x 15 x 1 cm² = 165 cm²

Question 2.
Find the total surface area of a cone, if its slant height is 21 m and diameter of its base is 24 m.
Solution:
Here, diameter = 24 m
Radius (r) = \(\frac{24}{2}\) m = 12m
Slant height (l) = 21 m
Total surface area = πr (r + l)

Question 3.
Curved surface area of a cone is 308 cm² and its slant height is 14 cm. Find:

1. radius of the base and
2. total surface area of the cone.

Solution:
Here, curved surface area = 308 cm²
Slant height (l) = 14 cm

1. Let the radius of the base be ‘r’ cm.
πrl = 308
\(\frac{22}{7}\) x r x 14 = 308
r = \(\frac{308×7}{22×14}\) = 7 cm
Thus, the required radius of the cone is 7 cm.

2. base area = πr² = \(\frac{22}{7}\) x 7² cm.
and curved surface area = 308 cm² given
∴ Total surface area = [Curved surface area] + [Base area]
= 308 cm² + 154 cm² = 462 cm²

Question 4.
A conical tent is 10 m high and the radius of its base is 24 m. Find

(i) slant height of the tent.
(ii) cost of the canvas required to make the tent, if the cost of 1 m² canvas is ₹ 70.

Solution:
h = 10 m
r =24m

Cost of canvas = CSA x Rate of canvas
= 1961.14 x 70
= ₹ 137279.8
= ₹ 137280.

Question 5.
What length of tarpaulin 3 m wide will be required to make conical tent of height 8 m and base radius 6 m? Assume that the extra length of material that will be required for stitching margins and wastage in cutting is approximately 20 cm. (Use π = 3.14)
Solution:

h = 8m
r = 6m
Width of tarpaulin = 3 m
Extra length required = 20 cm = 0.2 m

CSA of conical tent = πrl
= 3.14 x 6 x 10 = 188.4 m²
CSA of conical tent = Area of tarpaulin
188.4 = l x 3 (Here l = length of tarpaulin)
l = \(\frac{188.4}{3}\)
Total length of tarpaulin required = 62.8 + 0.2 = 63 m

Question 6.
The slant height and base diameter of a conical tomb are 25 m and 14 m respectively. Find the cost of white-washing its curved surface at the rate of ₹ 210 per 100 m².
Solution:
l = 25m
d = 14m
r = 7m
Rate of white washing = ₹ 210 per 100 m²
= \(\frac{210}{100}\) = ₹ 2.10 per m²
CSA of conical tomb = πrl
= \(\frac{22}{7}\) x 7 x 25 = 550 m²
Cost of white washing = Rate x CSA
= 2.10 x 550 (Rate per m² = \(\frac{220}{100}\))
= ₹ 1155

Question 7.
A joker’s cap is in the form of a right circular cone of base radius 7 cm and height 24 cm. Find the area of the sheet required to make 10 such caps.
Solution:
r = 7 cm
h = 24 cm

Area of sheet required = CSA of 10 such caps = 550 x 10 = 5500 cm².

Question 8.
A bus stop is barricaded from the remaining part of the road, by using 50 hollow cones made of recycled cardboard. Each cone has a base diameter of 40 cm and height 1 m. If the outer side of each of the cones is to be painted and the cost of painting is ₹ 12 per m² what will be cost of painting all these cones? (Use π = 3.14 and take \(\sqrt{1.04}\) =1.02).
Solution:
d = 40 cm
r = 20 cm = 0.20 m
h = l m
Rate = ₹ 12 per m²

= 1.02
CSA of cone = 3.14 x 0.2 x 1.02 = 0.64m²
Total area of 50 hollow cones= 50 x 0.64 = 32 m²
Cost of painting = 32 x 12 = ₹ 384
(Rate of painting = ₹ 12/m²)

MP Board Class 9th Maths Solutions

MP Board Class 9th General English Grammar Subject-Verb Concord

किसी sentence में जब subject का verb के साथ सही तालमेल होता है तभी वाक्य शुद्ध होता है। अर्थात् subject के वचन (number) तथा पुरुष (Person) के अनुसार ही verb में आवश्यक परिवर्तन किया जाना चाहिए।

जैसे-
Bird is flying in the sky.
Birds are flying in the sky.
I was singing
They were singing.

इस प्रकार के तालमेल के लिए निम्नलिखित नियम हैं
(1) दो या उससे अधिक Singular subject and से जोड़े जाएँ तो उनके साथ प्रायः Plural का verb आता है। जैसे
(i) Sita and Gita are twins.
(ii) You and your sister do this job well.

(2) यदि दो singular nouns (संज्ञाएँ) एक ही व्यक्ति या वस्तु का बोध कराती हैं, तो वहाँ singular verb का प्रयोग होता है। जैसे
(i) You and I am wrong.
(ii) My brother and guide has come.

(3) अगर singular कर्ता से पहले Each या Every का प्रयोग होता है तो singular verb का प्रयोग होता है। जैसे
(i) Every day brings hope.
(ii) Each student is prepared.

(4) Either….or, neither…..nor, के बाद हमेशा singular verb आती है। जैसे-
(i) Neither is he happy nor sad.
(ii) Either Ram or Shyam has done this work.

(5) यदि कर्ता को or, nor से जोड़ा जाए और वचन भिन्न हो तो बहुवचन की क्रिया (verb) का प्रयोग होता है। जैसे
(i) Either the boy or his friends have done this.

(6) Collective Noun के साथ पूरे समूह का भाव व्यक्त करने के लिए एकवचन क्रिया (verb) का प्रयोग करते हैं। परन्तु अगर एकवचन क्रिया का बोध कराना हो तो Plural verb का प्रयोग करते हैं। जैसे
(i) The police were chasing the thief.
(ii) The committee has decided this.

(7) जो Noun देखने में बहुवचन लगते हैं पर भाव में एकवचन ही होते हैं उनके साथ singular verb का प्रयोग करते हैं। जैसे
The wages of sin is death.

(8) कुछ Noun देखने में Singular लगते हैं परन्तु उनका अर्थ Plural होता है। उनके साथ Plural verb का प्रयोग करते हैं। जैसे
People are sad.

(9) कभी-कभी हम Verb का निकटतम Plural Subject के साथ मेल कर देते हैं। इस तरह वास्तविक subject की अनदेखी हो जाती है। हमें इस गलती से सावधान रहना चाहिए। जैसे-
(i) Neither of the women was present.
(ii) The quality of the oranges was good.

(10) Plural Noun जो किसी देश का नाम है या किताब का नाम है उसके बाद singular verb का प्रयोग होता है। जैसे
(i) The United States has a strong army.
(ii) The Gathering is a good novel.

Exercise-1

Fill in the blanks with correct words from those in brackets.
1. No news …………………….. bad news. (is/are)
2. The meeting …………………….. chosen a president. (has/have)
3. Each of the suspected men …………………….. been interrogated. (has/have)
4. Rice and curry …………………….. his favorite dish. (is/are)
5. All work and no play …………………….. Jack a dull boy. (make/makes)
Answer:
1. is,
2. has,
3. has,
4. are,
5. makes.

Exercise-2

Correct the following sentences.
1. Ten thousand rupees are a good sum.
2. Bread and butter are my food.
3. He and not you deserve this reward.
4. This pair of scissors are sharp.
5. Either you or your brother have done this.
6. The jury were of one mind.
7. None of them are rotten.
8. He as well as his parents are illiterate.
9. The king and poet are here.
10. Your spectacles is dirty.
Answer:
1. Ten thousand rupees is a good sum.
2. Bread and butter is my food.
3. He and not you deserve this reward.
4. This pair of scissors is sharp.
5. Either you or your brother has done this.
6. The jury was of one mind.
7. None of them is rotten.
8. He as well as his parents is illiterate.
9. The king and poet is here.
10. Your spectacles are dirty.

MP Board Class 9th English Solutions

MP Board Class 9th General English Letter Writing: Informal and Formal Letters

Informal Letters

Q. 1. Write a letter to your friend mentioning your hobbies.
Answer:
10, Raghava Pura, Ram Nagar,
Indore
10th Feb, 20…

Dear Neetu,
I am well here and hope the same for you. I want to share my hobbies with you as vacations are near. I am very fond of collecting stamps, visiting different places and listening to music. I am fond of travelling. I have visited many places like Gwalior, Agra, Mathura etc. I plan to visit Rajasthan in these vacations. More on meeting. Lots of regards to elders and love to youngers. Rest is O.K.

Waiting for your letter,

Yours
Rani

Q. 2. Write a letter to your friend informing him/her about your visit to your favourite park/ picnic spot.
Answer:
Ram Pal Singh 26/102,
Ashok Nagar, Kanpur
4-3-20….

Dear Raj,
I am fine here and hope the same at your end also. As our exams are over, what are your plans for your vacations? I am planning to go for a picnic to The Kanha Kisli National Park on 14th of this month. If you wish, you may also join us. Rest is fine. Pay my regards to elders and love to youngers.

Waiting for your letter,

Yours
Ramesh

Q. 3. Write a letter to your father to send you Rs. 500 as you have to pay your fees and buy some books and stationery.
Answer: .
Examination Hall
Bhopal,
15th July, 20….

Dear Father,
How are you and other family members? I am fine here busy with my studies. I have to pay my fees and buy some books and stationery. So kindly send me a sum of Rs. 500 soon. Convey my best regards to mother and lots of love to Pappu.

Yours loving
son Ashu

Q. 4. Write a letter to your friend inviting him on your birthday party.
Answer:
10, Prabhu Nagar Indore
20 March, 20….

Dear Raj,
Hope you are fine there. I am also in best of health. Today I am writing to you because I want to invite you in my birthday party on 28 March. Many of our friends will be coming. We shall enjoy a lot. It will be a great fiin. So please come definitely and inform me when are you coming here.

I shall wait for your reply.

Yours as ever Tarun

Q. 5. Write a letter to your friend congratulating him on his success in the examination.
Answer:
20, Shubham Colony
Bhopal (M.P.)
Dated 10 Aug, 20….

Dear Sonam,
Hearty congratulations to you. I am glad that you have got a brilliant success in the High School Examination. I saw your name in the merit list. We all became very happy to hear the news. You will have to give a nice dinner party to our friends when you come here.
Please inform me when you are reaching here.

Yours as ever
Anju

Q. 6. Write a letter to your father telling him about your hostel life.
Answer:
Nehru Hostel
Room No. 10
Chatarpur
Dated 10 July, 20….

Respected Father,
Warm Regards. Hope you are fine there. I am also fine here. You might be worried about me since I am residing in hostel. I wish to inform you that now I am settled here.

The hostel life is quite different from that at home. It is quite more disciplined. We have to wake up early in the morning and take care of our things -ourselves, do everything ourselves. My room mate is also very good and other boys in the hostel are also very co-operative. There are fixed timings of breakfast, lunch and dinner. The food that is served is of good quality. But I miss the taste of mom’s food. I miss home and everyone a lot. But I have adjusted here. Please don’t worry about me.

Give my regards to mom and love to Chhotu.

Yours obedient son
Rahul

Q. 7. Write a letter to your friend inviting him to attend the marriage ceremony of your brother.
Answer:
54, Shankar Shah Nagar,
Jabalpur
December 15,20….

Dear Rohan,
I hope this letter finds you in the best of health and happiness. You will be glad to know that the marriage of my elder brother has been fixed. The ceremony will take place on 30th December. You should come earlier. Mother remembered you and asked me to inform and invite you as she considers you also as her son. So, please come as soon as possible. There are lot of arrangements to be done and I would need your help and assistance. Please inform about your arrival.

Yours sincerely
Sumit

Q. 8. Write a letter to your younger brother advising him to take part in games regularly.
Answer:
10, Ashok Nagar
Lucknow
May 25,20….

Dear Himanshu,
Hope you are doing well there. Today I have received a letter from mother. She has also sent me your progress report. Though you are doing well in studies, but you are.not taking part in games. That is the reason that you are weak in health. I advise you to exercise regularly and take active part in games and sports. There is a saying ‘All work and no play makes Jack a dull boy’.

Write me soon about your health.

Yours affectionately
Nirmal

Formal Letters

Q. l. Write an application to your Head Master requesting him to sanction you a scholarship.
Answer:
To
The Headmaster,
Janta Junior School,
Gwalior

Respected Sir,
With due respect I beg to state that I am a student of your school. I study in class IX. My father is no more. He was the only supporter of my family. My mother is unable to have my study continued.

Therefore, I request you to sanction me scholarship to enable me to continue my studies. For this kind’favour I shall be highly obliged.

Thanking you,

Yours obediently
Mukul Jain
Roll No. 7
Class IX A
Dated : 10th October, 20…

Q. 2. Write an application to your Headmaster requesting him to provide you free text books.
Answer:
To
The Head Master,
Govt. Middle School
Bhopal

Respected Sir,
I beg to state that I am the student of your school studying in class IX. I belong to a very poor family. My father is a farmer. He is unable to bear the expenses of my studies. I am a very good student. I shall be highly obliged if you provide me free text books. Then only I shall be able to continue my studies.

Thanking you,
Yours obediently
Rahul Sharma
Roll No. 21
Class IX B
Dated : 6th July, 20….

Q. 3. Write an application to your Headmaster to grant you sick leave for three days.
Answer:
To
The Headmaster
Government Middle School,
Jabalpur

Subject : Application for sick leave for three days.

Sir,
Respectfully I beg to say that I am a student of IX-A. I am ill therefore I would be unable to attend the school. Kindly grant me leave for three days from 16 Oct., 2008 to 18 Oct., 2008.

I shall be thankful to you.

Yours obediently,
Manish Garg
Roll No. 16
Class IX-A
15 October, 2008

Q. 4. Write a letter to the district magistrate about nuisance caused by the use of loud speakers.
Answer:
31, AshishNagar
Sohagnagar
1st April, 20….

To,
The District Magistrate.
Sohagnagar

Sir,
I want to draw your attention to the nuisance caused by the use of loud-speakers. I am a student of graduation and my examinations are near. It is a time when all the students are busy day and night preparing for the examinations. Their success depends upon the proper use of their time and the concentration of their minds. It is regrettable that majority of citizens do not realise the importance of this time for students. They enjoy full liberty to use loud-speakers at their highest pitch to celebrate every occasion that comes to their hands. The result is that we are unable to make preparations in the right way.

I therefore request you to kindly impose a ban on the use of loud-speakers for the period of University Examinations and punish those who are found guilty.

Thanking you.
Yours faithfully
Raj Malhotra

Q. 5. Write a letter to M/s Shiva Furniture, Gwalior placing an order for school furniture.
Answer:
12, Modem Public School Datia (Gwalior) 10 March, 20….
To
M/s Shiva Furniture
Fort Road, Gwalior

Subject : Order for school furniture.

Dear Sirs,
Please send the following items of furniture for our public school at the above address. These items should be suitable for the age group of 10 to 14 years. It will be your responsibility that the items supplied by you should be of the specifications passed by M.P. Govt. Administration.
All the items should be sent through State Bank of India, Datia Branch.
1. Desks – 500
2. Chairs – 200
3. Stools – 500
4. Tables – 25

Yours faithfully
Manish Sharma
Manager

Q. 6. Write a letter to the Editor, Competition success to send you the magazine by post regularly every month.
Answer:
10, Jawahar Nagar,
Ratlam (M.P.)
Jan 30,20…. To,

The Manager
Competition Success
Delhi

Subject—Sending Competition Success every month.

Sir,
I wish to be a regular subscriber to your magazine competition success. I am enclosing herewith a cheque of Rs. 500/- as the annual subscription.
Please send me Competition Success on the above address regularly commencing from the February 20—issue.

Thanking you.

Yours faithfully
Ritu Das

Q. 7. Write a letter to the Director, Career Plus, 10, Kamla Park, Bhopal seeking information regarding their Postal Courses for computer science.
Answer:
20, Goel Market
Gwalior (M.P.)
July 4,20…. To,

The Director
Career Plus
10, Kamla Park
Bhopal

Subject : Information regarding 2 year Postal Course in Computer Science.

Sir,
I am a student of class IX of Modem Public School, Gwalior. I am interested in joining your career computer postal course. It would be kind of you, if you send me the following—

1. Information regarding your postal course :
(a) Charges for the whole course.
(b) Delivery of lessons, months and dates.
(c) Contact programmes, place dates.

2. Any other information regarding your postal course.

Hoping for an early reply.

Yours faithfully
Rahul Verma

MP Board Class 9th English Solutions

MP Board Class 9th General English Important Extracts from Poems

(Poem 1)

(A) When were you bom, O Light?
Who made you?
O Light, what are you?
What is your nature?
Are you wisdom’s daughter?
But Wisdom sleeps.

Questions:
(a) From which poem have these lines been taken?
(b) Who is the poem addressed to?
(c) Which questions arise in the poet’s mind about the birth of light?
Answers:
(a) These lines have been taken from the poem “O Light!”
(b) The poem is addressed to light.
(c) The questions that arise in the poet’s mind are
(i) When was light bom?
(ii) Who made light?
(iii) What is light’s nature?

(B) O Light, for how long have you befriended the sky?
And wherefore this love of it?
How do you completely merge in it?
She who made you all is a magician
She is enchanter, the bewitcher,
We praise her,
Prosper O Light.

Questions:
(a) What does the poet ask light about the sky?
(b) How much love does light show for the sky?
(c) Which names does the poet give to she (nature)?
Answers:
(a) The poet asks the light for how long has he befriended the sky.
(b) Light shows so much love for the sky that he merges himself into it.
(c) The poet gives these names to mother nature—a magician, an enchanter and a bewitcher.

2. (Poem 7)

Am I an adult or a child?
No ! Not an adult—I do not see
The reasons for adult disputes;
I am safe in non-understanding.
But does that mean that I am a child?
Well, am I a child or an adult?
No ! Not one or the other now;
One pace in front of childhood,
And one behind an adult.
Soon I shall stride into a new world,
The world of adult life.

Questions:
(a) What is the doubt in the poet’s mind?
(b) What is the poet unable to see?
(c) What is the present state of the poet?
Answers:
(a) The doubt in the poet’s mind is whether she is a child or an adult.
(b) The poet is unable to see the reasons for adult disputes.
(c) The poet is one pace in front of childhood and one behind an adult.

3. (Poem 11)

(A) One by one the casements catch
Her beams beneath the silvery thatch,
Couched in his kennel like a log,
With paws of silver sleeps the dog;

Questions:
(a) How do the windows catch the beams of the moon?
(b) How is the sound sleep of the dog described?
(c) Why do only the paws of the dog are silvery?
Answers:
(a) Windows catch moon beams one by one.
(b) The sound sleep of the dog is described as that he sleeps like a log.
(c) It is so because his whole body except for his paws is inside the Kennel, so only his paws look silvery.

(B) A harvest mouse goes scampering by,
With silver claws, and silver eye;
And moveless fish in the water gleam.
By silver reeds in silver stream.

Questions:
(a) From which poem have these lines been taken?
(b) How is the harvest mouse described in the poem?
(c) Who gleam in water? And where?
Answers:
(a) The extract has been taken from the poem ‘Silver’.
(b) The harvest mouse is described with silver , claws and silver eye.
(c) Moveless fish gleam in water by silver reeds in silver stream.

4. (Poem 15)

Woodman, forbear thy stroke !
Cut not its earth-bound ties;
Oh, spare that aged oak
Now towering to the skies !
When but an idle boy,
I sought its grateful shade;
In all their gushing joy
Here, too, my sisters played.

Questions:
(a) What does the poet ask the woodman?
(b) What did the poet do when he was an idle boy?
(c) What’ did his sisters do under the shade of the oak tree?
Answers:
(a) The poet asks the Woodman to forbear his ‘ stroke and not to cut its earth bound ties (i.e. roots)
(b) The poet sought the tree’s grateful shade when he was an idle boy.
(c) His sisters played under the shade of the tree.

5. (Poem 19)

(A) Full are my pitchers and far to carry
Lone is the way
Why, O why was I tempted to tarry
Lured by the boatmen’s song?
Swiftly the Shadows of Night are falling
Hear, O hear, is the white crane calling.

Questions:
(a) What fear does the poetess express?
(b) By what was she attracted?
(c) What was its result?
Answers:
(a) The poetess expresses the fear that her way is lonely.
(b) She was attracted by the boatman’s song.
(c) The result was that she got too late to return to her home.

(B) If in the darkness a serpent should bite me.
Or if an evil spirit should smite me,
Ram Re Ram I shall die.
My brother will murmur,
Why doth she linger?
My mother will wait and weep,
Saying, 0 safe may the great gods bring her.

Questions:
(a) Why does the poetess say “Ram Re Ram I shall die?”
(b) What will poetess’ brother think?
(c) What does the mother say?
Answers:
(a) The poetess says ‘Ram Re Ram I shall die because she fears that in darkness a serpent may bite her.
(b) Poetess’ brother will think why she lingers that is, why is she getting late.
(c) The mother prays great gods to bring her home safely.

MP Board Class 9th English Solutions

MP Board Class 9th Maths Solutions Chapter 13 Surface Areas and Volumes Ex 13.2

Assume π = \(\frac{22}{7}\) unless stated otherwise.

Question 1.
The curved surface area of a right circular cylinder of height 14 cm is 88 cm². Find the diameter of the base of the cylinder.
Solution:
h = 14 cm
CSA of cylinder = 88 cm²
CSA of cylinder = 2 πrh
88 = 2x \(\frac{22}{7}\) xr x 14
\(\frac{88}{4}\) = 2r
r = \(\frac{2}{2}\) = 1
Diameter = 2 r
= 1 x 2 = 2 cm.

Question 2.
It is required to make a closed cylindrical tank of height 1 m and base diameter 140cm from a metal sheet. How many square metres of the sheet are required for the same?
h = 1 m
d = 140 cm
r = 7o cm = 0.7 m
Area of metal required = TSA of cylinderical tank
= 2 πr (r + h)
= 2 x \(\frac{22}{7}\) x 0.7 (0.7 + 1)
= 4.4 x 1.7 = 7.4m²

Question 3.
A metal pipe is 77 cm long. The inner diameter of a cross section is 4 cm. the outer diameter being 4.4 cm. (see Fig.). Find its

(i) inner curved surface area.
(ii) outer curved surface area.
(iii) total surface area.

(iii) TSA = ICSA + OCSA + 2 x area of ring
= 968 + 1064.8 + 2 x 2.64
= 2032.8 + 5.28
= 20.38.08 cm².

Question 4.
The diameter of a roller is 84 cm and its length is 120 cm. It takes 500 complete revolutions to move once over to level a playground. Find the area of the playground in m².
Solution:
d = 84cm
∴ r = 42 cm
h = 120 cm
No. of revolution = 500
CSA of the roller = 2πrh
= 2 x \(\frac{22}{7}\) x 42 x 120
= 44 x 720
= 31680 cm²
Area of the playground = 31680 x 500
= 15840000 cm²
Area in m² \(\frac{ 15840000}{100 x 100}\)
= 1584 m².

Question 5.
A cylindrical pillar is 50 cm in diameter and 3.5 m in height Find the cost of painting the curved surface of the pillar at the rate of ₹ 12.S0 per m².
Solution:
d = 50cm
r = 25 cm²
h = 3.5 m = 350 cm
CSA of pillar = 2πrh
= 2x \(\frac{22}{7}\) x 25 x 350
= 44 x 1250
= 55000 cm²
CSA in m² = \(\frac{55000}{100×100}\)
Cost of painting the cylindrical pillar = ₹ 12.50 x 5.5
= ₹ 68.75

Question 6.
Curved surface area of a right circular cylinder is 4.4 m². If the radius of the base of the cylinder is 0.7 m, find its height.
Solution:
CSA = 4.4m².
r = 0.7 m
CSA of cylinder =2πrh
4.4 = 2x \(\frac{22}{7}\) x 0.7 x h
4.4 = 44 x 0.1 x h
4.4 = 4.4 x h
h = \(\frac{44}{4.4}\) = 1m

Question 7.
The inner diameter of a circular well is 3.5 m. It is 10 m deep. Find

1. its inner curved surface area
2. the cost of plastering this curved surface at the rate of ₹ 40 per m².

Solution:
d = 3.5m
r = 1.75 m
h = 10 m

1. ICSA of the well = 2πrh
= 2 x \(\frac{22}{7}\) x 1.75 x 10
= 110 m²

2. Cost of plastering = ₹ 40 x 110
= ₹ 4400.

Question 8.
In a hot water heating system, there is a cylindrical pipe of length 28 m and diameter 5 cm. Find the total radiating surface in the system.
Solution:
h = 28m
d = 5cm
r = 2.5cm = 0.025m
Total radiating surface = CSA of pipe = 2πrh
= 2 x \(\frac{22}{7}\) x 0.025 x 28
= 4.4 m².

9. Find

1. The lateral or curved surface area of a closed cylindrical petrol storage tank that is 4.2 m in diameter and 4.5 m high.

2. How much steel was actually used, if \(\frac{1}{2}\) of the steel actually used was wasted in making the tank.

Solution:
1. d = 4.2 m
r = 2.1m
h = 4.5 m
CSA of cylinderical tank = 2πrh
= 2x \(\frac{22}{7}\) x 2.1 x 4.5
= 59.4 m².
TSA = 2πrr(r + h)
= 2 x \(\frac{22}{7}\) x 2.1 (2.1 + 4.5)
= 2 x \(\frac{22}{7}\) x 2.1 x 6.6
= 44 x 1.98
= 87.12 m²

2. Let A be the area of sheet actually used
TSA = A – \(\frac{1}{12}\)

A = 95.04m².

Question 10.
In Fig. you see the frame of a lampshade. It is to be covered with a decorative cloth. The frame has a base diameter of 20 cm and height of 30 cm. Amargin of 2.5 cm is to be given for folding it over the top and bottom of the frame. Find how much cloth is required for covering the lampshade.
Solution:

d = 20 cm
r = 10 cm
h = 30 + 2.5 + 2.5 cm = 35 cm
Area of cloth required = CSA of cyliner of height 35 cm
= 2πrh
= 2 x \(\frac{22}{7}\) x 10 x 35
= 44 x 50 = 2200 cm².

Question 11.
The students of a Vidyalaya were asked to participate in a competi-tion for making and decorating penholders in the shape of a cylinder with a base, using cardboard. Each penholder was to be of radius 3 cm and height 10.5 cm. The Vidyalaya was to supply the competitors with cardboard. If there were 35 competitors, how much cardboard was required to be bought for the competition?
Solution:
r = 3 cm
h = 10.5 cm
Cardboard required for one penholder = CSA of penholder + Area of base
= 2πrh + πr²

MP Board Class 9th Maths Solutions