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.

Given :
Radius (r) of spherical balloon = 7 cm
Radius (R) of spherical balloon, when air is pumped into it = 14 cm

= \(\frac{Initial surface area}{Surface area after pumping air into balloon}\)
= \([\frac{4 × {\pi} × {r}^2}{4 × {\pi} × {R}^2}]\) \(= (\frac{r}{R})^2\)
= \((\frac{7}{14})^2 = \frac{1}{4}\)

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