Question

From a solid cylinder whose height is $4cm$ and radius $3cm$, a conical cavity of height $4cm$ and base radius $3cm$ is hollowed out. What is the volume of the remaining solid?

• A. $9\pi c{m}^3$
• B. $15\pi c{m}^3$
• C. $21\pi c{m}^3$
• D. $24\pi c{m}^3$

Answer 1

Answer: (D)

$24\pi c{m}^3$

The diameter of the cone and the cylinder is the same and height is also the same so volume of the remaining solid
$=$ Volume of the cylinder $-$ Volume of the cone
$=(\pi r^{2}h-\frac{1}{3}\pi r^{2}h)c{m}^3$
$=(\frac{2}{3}\cdot \pi r^{2}h)c{m}^3$
$=(\frac{2}{3}\pi .3^2.4)c{m}^3=24\pi c{m}^3$.