Question

Question 4
The radius of a spherical balloon increases from 7 cm to14 cm as air is being pumped into it. Find the ratio of surface areas of the balloon in the two cases.

Answer 1

Radius $r_1$ of spherical balloon = 7 cm

Radius $r_2$ of spherical balloon, when air is pumped in to it = 14 cm

$Requiredratio=\frac{Initialsurfacearea}{Surfaceareaafterpumpingairintotheballoon}=\frac{4\pi r_1^2}{4\pi r_2^2}={\left(\frac{r_1}{r_2}\right)}^2={\left(\frac{7}{14}\right)}^2=\frac{1}{4}$

The required ratio is 1:4.