Question

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

• A. $6.5$
• B. $5$
• C. $3.25$
• D. $4.5$

Answer 1

The correct option is A $6.5$

If a concentric hemisphere of half radius is removed from a hemispher of radius R then final solid is hollow hemispherical.

$\text{TSA of hollow hemisphere}=\pi (3R^2+r^2)=\pi (3R^2+(\frac{R}{2}{)}^2)=\frac{13}{4}\pi R^2$

$\text{CSA of removed hemisphere}=2\pi r^2=2\pi (\frac{R}{2}{)}^2=2\pi (\frac{R^2}{4})$

$\frac{\text{TSA of hollow hemisphere}}{\text{CSA of removed hemisphere}}=\frac{\frac{13}{4}\pi R^2}{2\pi \left(\frac{R^2}{4}\right)}=\frac{13}{2}=6.5$