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.

Answer 1

Radius (r₁) of spherical balloon = 7 cm 
Radius (r₂) of spherical balloon, when air is pumped into it = 14 cm
\(\text{Required ratio}=\frac{\text{Initial surface area}}{\text{Surface area after pumping air into the balloon}}\)
\(=\frac{4\pi r^2_1}{4\pi r^2_2}\)

\(=(\frac{r_1}{r_2})^2\)

\(=(\frac{7}{14})^2=\frac{1}{4}\)
Therefore, the ratio between the surface areas in these two cases is 1:4.