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NCERT Solutions for Class 9th Mathematics

 

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Chapter 13. Surface Areas and Volumes

Exercise 13.4

 

 

 

Exercise 13.4


Assume π = 22/7 , unless stated otherwise.

Q1. Find the surface area of a sphere of radius:

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

Solution:

Q2. Find the surface area of a sphere of diameter:

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

Solution:

(i) Surface area of sphere = 4πr2

Q3. Find the total surface area of a hemisphere of radius 10 cm. (Use π = 3.14)

Solution:

Total surface area of hemisphere = 3πr2

⇒ 3 × 3.14 × 10 × 10

⇒ 3 × 314

⇒ 942 cm2

Q4. 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:

Surface area of sphere = 4πr2

Q5. 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:

Curved surface area of hemisphere = 2πr2  

Q6. Find the radius of a sphere whose surface area is 154 cm2.

Solution:

Area = 154 cm2

Surface area of sphere = 4πr2

Q7. The diameter of the moon is approximately one fourth of the diameter of the earth. Find the ratio of their surface areas.

Solution:

Let the diameter of earth = x

Q8. 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:

Inner radius = 5 cm,    width = 0.25 cm,   radius = 5.25 cm

Curved surface area of hemisphere = 2πr2

⇒ 44 × 0.75 × 5.25

⇒ 173.25

Q9. A right circular cylinder just encloses a sphere of

radius (see Fig. 13.22). Find

(i) surface area of the sphere,

(ii) curved surface area of the cylinder,

(iii) ratio of the areas obtained in (i) and (ii).  

Solution:

Radius of sphere = r,   radius of cylinder = r + r = 2r

(i) surface area of sphere = 4πr2

(ii) curved surface area of cylinder = 2πrh

⇒ 2πr(2r)

 4πr2

 

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