Question

The radius of a spherical balloon increases from $7cm$ to $14cm$ as air is being pumped into it. Find ratio of surface areas of the balloon in the two cases.

Answer 1

Total surface are (TSA) of balloon having radius $r$ is given as $4\pi r^2$

Let radius of spherical balloons be $r_1$ and $r_2$ ,

Here $r_1=7cm$ and $r_2=14cm$
Ratio of surface area
$=\frac{TSAoffirstballoon}{TSAofpumpedballoon}$
$=\frac{4\pi r_1^2}{4\pi r_2^2}$
$=\frac{(7{)}^2}{(14{)}^2}=(\frac{1}{2}{)}^2$
$=\frac{1}{4}$
$\therefore$ Ratio of surface areas of the balloons $=1:4$