Question

The total surface areas of two hemispheres are in the ratio 1:4. Find the ratio of their volumes.
[2 Marks]

Answer 1

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

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

r : R = 1 : 2.
[1 Mark]

Now, the ratio of volumes of two hemispheres = $\frac{2}{3}$$\pi$$r^3$ : $\frac{2}{3}$$\pi$$R^3$

$r^3$ : $R^3$ = $1^3$ : $2^3$ = 1:8
[1 Mark]