Question

If the volume of a hemisphere is four times its total surface area, then find its radius
(in cm)?

• A. 18

Answer 1

The correct option is A 18

We know that,
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,
Volume of hemisphere=TSA of hemisphere
$\therefore \frac{2}{3}\pi r^3=4\times 3\pi r^2$

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

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

$\Rightarrow r=18cm$