## MP Board Class 9th Maths Solutions Chapter 13 Surface Areas and Volumes Ex 13.8

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

Question 1.

Find the volume of a sphere whose radius is

(i) 7 cm

(ii) 0.63 m

Solution:

(i) Here, radius (r) = 7 cm

∴ Volume of the sphere

Thus, the required volume is 1.05 m^{3} (approx.)

Question 2.

Find the amount of water displaced by a solid spherical ball of diameter

(i) 28 cm

(ii) 0.21 m

Solution:

(i) Diameter of the ball = 28 cm

Question 3.

The diameter of a metallic ball is 4.2 cm. What is the mass of the ball, if the density of the metal is 8,9 g per cm^{3}.

Solution:

d = 4.2 cm

⇒ r = 2.1 cm

Density (D) = 8.9 gm/cm^{3}

Volume of metallic ball = \(\frac{4}{3}\) x \(\frac{22}{7}\) x 2.1 x 2.1 x 2.1 = 38.808 cm^{3}

Mass = D x V

= 8.9 x 38.808

= 345.3912 gm.

Question 4.

The diameter of the moon is approximately one – fourth of the diameter of the earth. What fraction of the volume of the earth is volume of the moon?

Solution:

Let d and d be the diameter of moon and earth respectively.

Question 5.

How many liters of milk can hemispherical bowl of diameter 10 J cm hold?

Solution:

d = 10.5 cm

r = 5.25 cm

Volume of the hemisphere = \(\frac{2}{3}\) x \(\frac{22}{7}\) x 5.25 x 5.25 x 0.25

= 303.18 cm^{3}

= 0.303 l

Question 6.

A hemispherical tank is made up of an iron sheet 1cm thick. If the inner radius is 1 m, then find the volume of the iron used to make the tank.

Solution:

t = 1 cm

r_{1} = 1 m = 100 cm

r_{2} = r_{1} + t = 100 + 1 = 101 cm

Outer volume of tank (V_{2}) = \(\frac{2}{3}\) πr_{2}^{2}

Inner volume of tank (V_{1}) = \(\frac{2}{3}\) πr_{1}^{3}

Volume of iron = Outer volume – inner volume

= 0.06348 ml

Question 7.

Find the volume of a sphere whose surface area is 154 cm2.

Solution:

Surface area = 154 cm^{2}

Surface area of sphere = 4πr^{2}

Question 8.

A dome of a building is in the from of a hemisphere. From inside, it was White – washed at the cost of ₹ 498.96. If the cost of white-washing is ₹ 2.00 per square meter, find the

(i) inside surface area of the dome.

(ii) volume of the air inside the dome.

Solution:

(i) Cost = ₹ 498.96

Rate = ₹ 2 per m^{2}

Inside surface area = \(\frac{498.96}{2}\) = 249.48 m^{2}

Inside curved surface area = 2πr^{2}

Question 9.

Twenty seven solid iron spheres, each of radius r and surface area S are melted to form a sphere with surface area S’. Find the

(i) radius r’ of the new sphere

(ii) ratio of S and S’.

Solution:

Let V and be the volume of old and new sphere respectively

(i) Volume of new sphere = 27 x volume of old sphere

V_{1} = 27 x V

Question 10.

A capsule of medicine is in the shape of a sphere of diameter 3.5 mm. How much medicine (in mm^{3}) is needed to fill this capsule?

Solution:

d = 3.5 mm

r = 1.75 mm

Volume of medicine needed to fill the capsule

= \(\frac{4}{3}\)πr^{3}

= \(\frac{4}{3}\) x \(\frac{22}{7}\) x 1.75 x 1.75 x 1.75

= 22.458 mm^{3}

= 22.46 mm^{3} (Approx.)