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 of the balloon before pumping air (r₁) = 7 cm

Radius of the balloon after pumping air (r₂) = 14 cm

Initial surface area = 4πr₁²

Surface area after pumping air into ballon = 4πr₂²

Ratio = $\dfrac{\text{Initial surface area}}{\text{Surface area after pumping air into ballon}}$

$= \dfrac{4πr$1^2}{4πr2^2} \\[1em] = \dfrac{r1^2}{r2^2} \\[1em] = \Big(\dfrac{r1}{r2}\Big)^2 \\[1em] = \Big(\dfrac{7}{14}\Big)^2 \\[1em] = \Big(\dfrac{1}{2}\Big)^2 \\[1em] = \dfrac{1}{4} \\[1em] = 1 : 4.

Hence, the ratio of the surface area of the balloons = 1 : 4.