Question

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 balloon in the two cases.

Answer 1

It is given that $,$

The radius of a spherical balloon increases from $7cm$ to $14cm$

let $r_1=7cm$

and $r_2=14cm$

We know that surface area of sphere $=4{\mathrm{\pi r}}^2$

Ratio of their surface area $=\frac{4{{\mathrm{\pi r}}_1}^2}{4{{\mathrm{\pi r}}_2}^2}$

$={\left(\frac{r_1}{r_2}\right)}^2$

$={\left(\frac{7}{14}\right)}^2$

$={\left(\frac{1}{2}\right)}^2$

$=\frac{1}{4}$

Hence, the ratio of surface areas of the balloon in the two cases are $1:4$ .