Question

The radius of a spherical balloon increases from $7cm$ to $14cm$ as air is pumped into it. Find the ratio of the volumes of the balloon before and after pumping the air.

Answer 1

Formula for volume of sphere with radius $r$ is given by
$V=\frac{4}{3}\pi r^3$.
Given initial radius of spherical ballon $=r_1=7cm$
Final radius $r_2=14cm$.
Ratio of volumes of balloon before and after pumping the air.
$\frac{V_1}{V_2}=\frac{\frac{4}{3}\pi (r_1{)}^3}{\frac{4}{3}\pi (r_2{)}^3}$
$=\frac{(r_1{)}^3}{(r_2{)}^3}$
$=\frac{7^3}{{14}^3}$
$=\frac{7\times 7\times 7}{14\times 14\times 14}$

$=\frac{1}{8}$
Therefore, ratio of volumes $=1:8$