Question

If the volume of a hemisphere is four times its total surface area, the radius is

• A. 21 cm
• B. 9 cm
• C. 18 cm

Answer 1

The correct option is C 18 cm

The volume of a hemisphere of radius $rcm$ = $\frac{2}{3}\pi r^3$

TSA of a hemisphere of the same radius = $3\pi r^2$.

Given that $\frac{2}{3}\pi r^3$ = $4\times 3\pi r^2$

$\Rightarrow \frac{1}{3}\pi r$ = $6\pi$

$\Rightarrow \frac{1}{3}r$ = $6$

$\Rightarrow r=18cm$