Question

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 two cases.

Answer 1

Given radius $r_1=7cm$

$r_2=14cm$

Initial surface area $(r_1=7)=4\pi r^2$

$=4\times \frac{22}{7}\times 7\times 7$

$=616c{m}^2$

Surface area $(r_2=14)=4\pi r^2=4\times \frac{22}{7}\times 14\times 14$

$=2464c{m}^2$

Ratio of surface area $=\frac{616}{2464}=\frac{1}{4}$