The volumes of two spheres are in the ratio 64:27 Find the ratio of their surface areas - Maths -

Question

The volumes of two spheres are in the ratio 64:27 Find the ratio
of their surface areas

Aakash Sharma · Accepted Answer

Let radius of the two given spheres be R and r respectively.

Given : Ratio of volumes = 64 : 27

$\Rightarrow \frac{\frac{4}{3} π R^{3}}{\frac{4}{3} π r^{3}} = \frac{64}{27} \Rightarrow {(\frac{R}{r})}^{3} = \frac{64}{27} \Rightarrow \frac{R}{r} = \frac{4}{3}$

Now, Ratio of surface area = 4 $π$ R²: 4 $π$ r²

$\Rightarrow \frac{4 π R^{2}}{4 π r^{2}} = (\frac{R}{r})^{2} = (\frac{4}{3})^{2} = \frac{16}{9}$

∴ Ratio of surface areas = 16 : 9

The volumes of two spheres are in the ratio 64:27. Find the ratio of their surface areas