Question

The radius of solid sphere is $R$. If a solid sphere of radius $\frac{R}{2}$ is removed from it. Find the volume of shell formed.

• A. $\frac{7}{6}\pi R^3$
• B. $\frac{6}{7}\pi R^3$
• C. $\frac{7}{5}\pi R^3$
• D. $\frac{7}{8}\pi R^3$

Answer 1

The correct option is A $\frac{7}{6}\pi R^3$

Volume of shell $=\frac{4}{3}\pi (r_2^3-r_1^3)$
The shell formed has the outer radius$\left(r_2\right)$ of $R$ and inner radius$\left(r_1\right)$ of $\frac{R}{2}$.
$=\frac{4}{3}\pi (R^3-(\frac{R}{2}{)}^3)=\frac{4}{3}\pi (R^3-\left(\frac{R^3}{8}\right))=\frac{7}{6}\pi R^3$