Question

From a solid right circular cylinder with height $h$ and radius of the base $r$, a right circular cone of the same height and same base is removed. Find the volume of the remaining solid.

• A. $\frac{2}{3}\pi r^{2}h$
• B. $\pi r^{2}h$
• C. $2\pi r^{2}h$
• D. $\frac{1}{3}\pi r^{2}h$

Answer 1

The correct option is A $\frac{2}{3}\pi r^{2}h$

Volume of the remaining solid $=$ Volume of cylindrical section $-$ Volume of conical shape.

So, Volume of the material removed $=\pi r^{2}h-\frac{1}{3}\pi r^{2}h=\frac{2}{3}\pi r^{2}h$