The radius of a spherical balloon increases from 7cm to 14cm as air is being pumped into it. Find the ratio of surface areas of the original balloon to the resulting new balloon.

Explanation

We assume that `r` and `R` be the radii of spherical balloon and spherical balloon when air is pumped into it respectively.

Let `r=7cm` and `R=14cm`

Required ratio of surface area = (initial surface area)/(Surface area after pumping air into balloon)

Required ratio of surface area = `4pi7^2/4pi14^2`

= `49/196`=`1/4`

Hence, the ratio between the surface areas are `1:4`.