Question

Volume and total surface area of a solid hemisphere are equal. Find the radius of hemisphere

• A. $3cm$
• B. $4cm$
• C. $4.5cm$
• D. $5.5cm$

Answer 1

The correct option is C $4.5cm$

Let the radius of hemisphere be $r$

The volume of hemisphere is $\frac{2}{3}\pi r^3$

The surface area of hemisphere is $2\pi r^2=\pi r^2=3\pi r^2$

Given that both are equal

$\Rightarrow \frac{2}{3}\pi r^3=3\pi r^2$

$\Rightarrow r=\frac{9}{2}=4.5$

Therefore the correct option is $C$