Question

Volume of two sphere are in the ratio $64:27$. Find the ratio of their surface area.

Answer 1

Given that,

Volume of two sphere are in ratio$=64:27$

We know that ,

Volume of sphere$=\frac{4}{3}\pi r^3$

Then,

$\frac{Volumeofsphere\left(1\right)}{Volumeofsphere\left(2\right)}=\frac{64}{27}$

$\frac{\frac{4}{3}\pi {r_1}^3}{\frac{4}{3}\pi {r_2}^3}=\frac{64}{27}$

$\frac{{r_1}^3}{{r_2}^3}=\frac{64}{27}$

$\frac{r_1}{r_2}=\frac{4}{3}$

Then, Ratio of areas both spheres

$\frac{areaofsphere\left(1\right)}{areaofsphere\left(2\right)}=\frac{4\pi {r_1}^2}{4\pi {r_2}^2}$

$=\frac{{r_1}^2}{{r_2}^2}$

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

$={\left(\frac{4}{3}\right)}^2$

$=\frac{16}{9}$

Hence, this is the answer.