Question

The surface areas of two spheres are in the ratio 1 : 4. Find the ratio of their volumes.

Answer 1

Sol:
Given that surface areas of two spheres are in the ratio 1:4.

$\frac{4}{3}$$\pi$$r^2$ : $\frac{4}{3}$$\pi$$R^2$ = 1 : 4

r : R = 1 : 2.

Now ratio of volumes of two spheres = $\frac{4}{3}$$\pi$$r^3$ : $\frac{4}{3}$$\pi$$R^3$

$r^3$ : $R^3$ = $1^3$ : $2^3$ = 1:8