Question

Chapter Surface area and volume

Q1 Find volume of sphere whose surface area is 154cm2

Q2 Find the volume of the right circular cone with (i) radius 6 cm (ii) radius 3.5 height 12cm​

Answer 1

Question 1

Surface area of sphere = 154 cm2

= 4πr^2 = 154

= 4/1 × 22 \7 × r^2 = 154

= r^2 = 154/22 × 7/4 ( transpose )

=r^2 = (7/2)^2 ( By cancellation)

Positive root on both sides

√r^2 = √ (7/2)^2

r = 7/2

Volume of sphere = 4/3× π × r^3

= 4\3 ×22/7 × 7/2 × 7/2 × 7/2

= 11 × 7 × 7 / 3 ( By cancellation)

= 179.6 cm^3

Question 2

Given:-

(i) radius 6 cm

(ii) radius 3.5 height 12cm

Solution:-

Volume of cone

= 1/3 × π × r^2 ×h

= 1/3 × 22/7 × 6^2 × 6

= 22 × 12 ( By cancellation )

= 264 cm ^3

Formula used :-

4/3 π r^3 ( Volume of sphere )

1/3 × π × r^2 ×h ( Volume of cone)

Note :-

Pie is taken as 22/7