Question

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

• A. $21cm$
• B. $12cm$
• C. $9cm$
• D. $18cm$

Answer 1

The correct option is C

$9cm$

The volume of a hemisphere of radius $rcm$ = $\frac{4}{3}\pi r^3$

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

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

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

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

$\Rightarrow r=9cm$