Question

From a cylinder whose height is 8 cm and radius is 6 cm, a conical cavity of height 8 cm and base radius 6 cm is hollowed out. Find the volume of the remaining solid. $(\pi =\frac{22}{7})$.

Answer 1

Given that, the height $\left(h\right)$ of the cylinder is $8cm$ and radius $\left(r\right)$ is $6cm$.

From this cylinder, a conical cavity of same height and radius is cut.

To find out: Volume of the remaining solid.

Volume of the remaining solid $=$ Volume of cylinder $-$ Volume of the conical cavity.

We know that,

Volume of a cylinder $=\pi r^{2}h$

and volume of a cone $=\frac{1}{3}\times \pi r^{2}h$

$\therefore$ Volume of remaining solid $=\pi r^{2}h-\frac{1}{3}\pi r^{2}h$

$=\frac{2}{3}\pi r^{2}h$

$\Rightarrow \frac{2}{3}\times \frac{22}{7}\times 6\times 6\times 8[\because \pi =\frac{22}{7}]$

$=\frac{12672}{21}$

$=603.43c{m}^3$

Hence, the volume of the remaining solid is $603.43c{m}^3$.