Question

If a concentric hemisphere of radius $\frac{R}{2}$ is removed from a radius of hemisphere $R$. Find the ratio of remaining volume to that of removed.

• A. 5
• B. 6
• C. 7
• D. 8

Answer 1

The correct option is C 7

$\text{Remaining volume}=\frac{2}{3}\pi (R^3-(\frac{R}{2}{)}^3)=\frac{2}{3}\pi (R^3-\left(\frac{R^3}{8}\right))=\frac{7}{12}\pi R^3$

$\text{Removed volume}=\frac{2}{3}\pi \left(\frac{R^3}{8}\right)$

$\frac{\text{Remaining volume}}{\text{Removed volume}}=\frac{\frac{7}{12}\pi R^3}{\frac{2}{3}\pi \left(\frac{R^3}{8}\right)}=7$