Question

The diameter of a spherical balloon increases from $14cm$ to $28cm$ as air is being pumped into it. Find the ratio of surface areas of the balloons in the two cases.

Answer 1

Given the diameter of the small balloon is $14cm$ and diameter bigger balloon is $28cm$

Then the radius of small balloon =$\frac{14}{2}=7cm$

And radius of bigger balloon=$\frac{28}{2}=14cm$

We know the Surface area of balloon $=4\pi r^2$

Then the ratio of the surface area of two balloons =$\frac{4\pi (7{)}^2}{4\pi (14{)}^2}$

$=\frac{49}{196}$

$=\frac{1}{4}$

Then the ratio of both balloon $=1:4$