# The radius of a spherical balloon increases from 7 cm to 14 cm as air is being pumped into it.

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 the two cases.

Solution:

Radius (r1) of spherical balloon = 7 cm

Radius (r2) of spherical balloon, when air is pumped into it = 14 cm

Required ratio $=\frac{\text { Initial surface area }}{\text { Surface area after pumping air into balloon }}$

$=\frac{4 \pi r_{1}^{2}}{4 \pi r_{2}^{2}}=\left(\frac{r_{1}}{r_{2}}\right)^{2}$

$=\left(\frac{7}{14}\right)^{2}=\frac{1}{4}$

Therefore, the ratio between the surface areas in these two cases is $1: 4$.