Ex 13.8 NCERT Solutions Class 9 Chapter 13


The solutions to exercise 13.8 (from class 9th's maths NCERT book) are given below. The exercise has 10 questions that have been explained thoroughly with proper reasoning. 




Volume of the sphere

=  4/3 x Ï€ r 3 

= 4/3 x 22/7 x 7 x 7 x 7

= 88/3 x 49

= 1437.33 cm 3

Volume of the sphere

=  4/3 x Ï€ r 3 

=  4/3 x 22/7 x 0.63 x 0.63 x 0.63

 =  4 x 22 x 0.09 x 0.21 x 0.63

= 1.048 cm 3

(i) the Volume of the sphere

=  4/3 x Ï€ r 3

=  4/3 x 22/7 x 14 x 14 x 14

=  88/3 x 2 x 14 x 14

= 11498.67 cm 3


(ii) Volume of the sphere

=  4/3 x Ï€ r 3

=  4/3 x 22/7 x 0.105 x 0.105 x 0.105

= 4 x 22 x 0.05 x 0.105 x 0.105

= 0.04851 cm 3


Volume of the sphere

=  4/3 x Ï€ r 3

= 4/3 x 22/7 x 2.1 x 2.1 x 2.1 

= 4 x 22 x 0.1 x 2.1 x 2.1

= 38.808 cm 3

Mass of 1 cm 3 = 8.9 g

Mass of 38.808 cm 3 = 8.9 x 38.808

= 345.49 g

Diameter of moon

= ¼ the diameter of earth

If radius of earth is r

Radius of moon is r/4

Volume of moon : Volume of earth

 4/3 x Ï€ (r/4)  : 4/3 x Ï€ r 3

(1/64) : 1 

1: 64


Volume of hemispherical bowl

= 2/3 x π r 3

= ⅔ x 22/7 x 5.25 x 5.25 x 5.25

= 2 x 22 x 0.25 x 5.25 x 5.25

= 303.1875 cm 3

= 0.303 liters



Volume of outer hemisphere - Volume of inner hemisphere

= 2/3 x π r 3 -- 2/3 x π r 3

= 2/3 x 22/7 ( 1.01 3 - 1 3)

= 0.06348

SA of sphere = 4 π r 2

154 = 4 x 22/7 x  r 2

49/4 = r 2

7/2 = r


Volume of the sphere

= 4/3 x π r 3

= 4/3 x 22/7 x 3.5 x 3.5 x 3.5

= 179.66  cm3

Rs 2 is the cost of painting = 1 m2 area

Rs 498.96 is the cost of painting =

498.96/2 = 249.48 m2 area



Therefore inside surface area of the hemisphere is 

= 249.48 m

CSA of hemisphere = 2 x 22/7 x  r 2

249.48 =44/7 x   r 2

39.69 =   r 2

r= 6.3 m

Volume of the hemisphere: 

= 2/3x 22/7 x  r 3

= 2/3 x 22/7 x 6.3 x 6.3 x 6.3

= 44 x 0.3 x 6.3 x 6.3

= 523.908  m 3



(i) Volume of the new sphere = 27 x volume of small spheres

4/3x 22/7 x r’3  = 27 x 4/3x 22/7 (r)3


r’ 3  = 27 x (r)3

r’ 3  = 3 3  x (r)3

r’ 3  = (3 r)3

r’ = 3 r



(ii) Surface area of big sphere : Surface area of small sphere

4 x Ï€ r’ 2   : 4 x Ï€ r 2

r’ 2   : r 2

r 2 : (3 r’)

r 2 : 9 r’

1 : 9

Volume of the capsule

= 4/3x 22/7 x r3

= 4/3x (22/7) x 1.75 x 1.75 x 1.75 

= 22.458 mm3