## EXERCISE 13.8

#### Page No 236:

#### Question 1:

Find the volume of a sphere whose radius is

(i) 7 cm (ii) 0.63 m

#### Answer:

(i) Radius of sphere = 7 cm

Volume of sphere =

Therefore, the volume of the sphere is 1437 cm^{3}.

(ii) Radius of sphere = 0.63 m

Volume of sphere =

Therefore, the volume of the sphere is 1.05 m^{3} (approximately).

#### Question 2:

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

(i) 28 cm (ii) 0.21 m

#### Answer:

(i) Radius (*r*) of ball =

Volume of ball =

Therefore, the volume of the sphere is cm^{3}.

(ii)Radius (*r*) of ball = = 0.105 m

Volume of ball =

Therefore, the volume of the sphere is 0.004851 m^{3}.

#### 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}?

#### Answer:

Radius (*r*) of metallic ball =

Volume of metallic ball =

Mass = Density × Volume

= (8.9 × 38.808) g

= 345.3912 g

Hence, the mass of the ball is 345.39 g (approximately)

#### 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 the volume of the moon?

#### Answer:

Let the diameter of earth be *d*. Therefore, the radius of earth will be .

Diameter of moon will be and the radius of moon will be .

Volume of moon =

Volume of earth =

Therefore, the volume of moon is of the volume of earth

#### Question 5:

How many litres of milk can a hemispherical bowl of diameter 10.5 cm hold?

#### Answer:

Radius (*r*) of hemispherical bowl** = **= 5.25 cm

Volume of hemispherical bowl =

= 303.1875 cm^{3}

Capacity of the bowl =

Therefore, the volume of the hemispherical bowl is 0.303 litre

#### Question 6:

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

#### Answer:

Inner radius (*r*_{1}) of hemispherical tank = 1 m

Thickness of hemispherical tank = 1 cm = 0.01 m

Outer radius (*r*_{2}) of hemispherical tank = (1 + 0.01) m = 1.01 m

#### Question 7:

Find the volume of a sphere whose surface area is 154 cm^{2}.

#### Answer:

Let radius of sphere be *r*.

Surface area of sphere = 154 cm^{2}

⇒ 4π*r*^{2} = 154 cm^{2}

Volume of sphere =

Therefore, the volume of the sphere is cm^{3}.

#### Question 8:

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

(i) inside surface area of the dome,

(ii) volume of the air inside the dome.

#### Answer:

(i) Cost of white-washing the dome from inside = Rs 498.96

Cost of white-washing 1 m^{2} area = Rs 2

Therefore, CSA of the inner side of dome =

= 249.48 m^{2}

(ii) Let the inner radius of the hemispherical dome be *r*.

CSA of inner side of dome = 249.48 m^{2}

2π*r*^{2} = 249.48 m^{2}

⇒ *r* = 6.3 m

Volume of air inside the dome = Volume of hemispherical dome

= 523.908 m^{3}

= 523.9 m^{3} (approximately)

Therefore, the volume of air inside the dome is 523.9 m^{3}.

#### 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’.

#### Answer:

(i)Radius of 1 solid iron sphere = *r*

Volume of 1 solid iron sphere

Volume of 27 solid iron spheres

27 solid iron spheres are melted to form 1 iron sphere. Therefore, the volume of this iron sphere will be equal to the volume of 27 solid iron spheres. Let the radius of this new sphere be *r*‘.

Volume of new solid iron sphere** **

(ii) Surface area of 1 solid iron sphere of radius* r* = 4π*r*^{2}

Surface area of iron sphere of radius *r*‘ = 4π (*r*‘)^{2}

= 4 π (3*r*)^{2} = 36 π*r*^{2}

#### 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?

#### Answer:

Radius (*r*) of capsule

Volume of spherical capsule

**= **

= 22.458 mm^{3}

= 22.46 mm^{3} (approximately)

Therefore, the volume of the spherical capsule is 22.46 mm^{3}