Question

A rocket is in the shape of a cone mounted on a right circular cylinder, their common base diameter is $8\text{cm}.$ The height of cylindrical and conical shapes are $6\text{cm}$ and $3\text{cm}$ respectively. Find the volume of the rocket.

Answer 1

For conical part,

Diameter, $d=8\text{cm}$

Radus, $r=4\text{cm}$

Height, $h=3\text{cm}$

$\begin{array}{cc}\text{Volume of conical part}& =\frac{1}{3}\pi r^{2}h\\ & =\frac{1}{3}\pi {\left(4\right)}^2\left(3\right)\\ & =16\pi {\text{cm}}^3\end{array}$

For cylindrical part,

Diameter, $d=8\text{cm}$

Radus, $r=4\text{cm}$

Height, $h=3\text{cm}$

$\begin{array}{cc}\text{Volume of cylindrical part}& =\pi r^{2}h\\ & =\pi {\left(4\right)}^2\left(6\right)\\ & =96\pi {\text{cm}}^3\end{array}$

Hence, the total volume of the rocket will be,

Volume of rocket $=$ Volume of conical part $+$ Volume of cylindrical part

$=16\pi +96\pi$

$=112{\text{cm}}^3$