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.

$\left[2\right]$

Answer 1

$\text{Remaining volume}=\frac{2}{3}\pi (R^3-(\frac{R}{2}{)}^3)=\frac{2}{3}\pi (R^3-\left(\frac{R^3}{8}\right))=\frac{7}{12}\pi R^3$
$\left[1\right]$


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

$\frac{\text{Remaining volume}}{\text{Removed volume}}=\frac{\frac{7}{12}\pi R^3}{\frac{2}{3}\pi \left(\frac{R^3}{8}\right)}=7$
$\left[1\right]$