Question

Volume and total surface area of a solid hemisphere are equal in magnitude. The volume is expressed in cm${}^3$ and the area is expressed in cm${}^2$. Find the radius of hemisphere.

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

Answer 1

The correct option is C $4.5$ cm

Volume of a hemisphere of radius '$r$' $=\frac{2}{3}\pi r^3$
Total Surface Area of a hemisphere of radius '$r$' $=3\pi r^2$
According to the question, we have
$\frac{2}{3}\pi r^3=3\pi r^2$
$\Rightarrow \frac{2}{3}\times r=3$
$\Rightarrow r=\frac{9}{2}=4.5$
Hence, option 'C' is correct.