Exercise 13.8 - Chapter 13 - Surface Areas & Volumes - Ncert Solutions class 9 - Maths

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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 cm³.

(ii) Radius of sphere = 0.63 m

Volume of sphere = 

Therefore, the volume of the sphere is 1.05 m³ (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 cm³.

(ii)Radius (r) of ball = = 0.105 m

Volume of ball = 

Therefore, the volume of the sphere is 0.004851 m³.

 

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 cm³? 

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 cm³

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 (r₁) of hemispherical tank = 1 m

Thickness of hemispherical tank = 1 cm = 0.01 m

Outer radius (r₂) of hemispherical tank = (1 + 0.01) m = 1.01 m

Question 7:

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

Answer:

Let radius of sphere be r.

Surface area of sphere = 154 cm²

⇒ 4πr² = 154 cm²

Volume of sphere = 

Therefore, the volume of the sphere is  cm³.

 

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 m² area = Rs 2

Therefore, CSA of the inner side of dome = 

= 249.48 m²

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

CSA of inner side of dome = 249.48 m²

2πr² = 249.48 m²

⇒ r = 6.3 m

Volume of air inside the dome = Volume of hemispherical dome

= 523.908 m³

= 523.9 m³ (approximately)

Therefore, the volume of air inside the dome is 523.9 m³.

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 = 4πr²

Surface area of iron sphere of radius r‘ = 4π (r‘)²

= 4 π (3r)² = 36 πr²

Question 10:

A capsule of medicine is in the shape of a sphere of diameter 3.5 mm. How much medicine (in mm³) is needed to fill this capsule?

Answer:

Radius (r) of capsule 

Volume of spherical capsule 

= 

= 22.458 mm³

= 22.46 mm³ (approximately)

Therefore, the volume of the spherical capsule is 22.46 mm³.