Question

A rocket is in the shape of a cylinder with a cone attached to one end and a hemisphere attached to the other. All of them are of the same radius of $1.5$m. The total length of the rocket is $7$m and height of the cone is $2$m. Calculate the volume of the rocket.

Answer 1

Given :

Radius $r=1.5m$, Total length =$7m$

Height of the cone $\left(h_1\right)=2m$

Height of hemisphere $=$ Radius of hemisphere $=1.5m$

Height of cylinder $\left(h_2\right)=$ Total length $-h_1-r=7-2-1.5=3.5m$

Now, volume of the rocket $=$ Volume of the cylinder $+$ volume of a cone $+$ volume of a hemisphere ........ $\left(i\right)$

We know that, Volume of the cylinder $=\pi r^2{h}_2$

$=\pi (1.5{)}^2\times 3.5$

$=7.875\pi m^3$

Volume of a cone $=\pi r^2\frac{h_1}{3}$

$=\pi (1.5{)}^2\times \frac{2}{3}$

$=1.5\pi m^3$

Volume of a hemisphere $=\frac{2}{3}\pi r^3$

$=\frac{2}{3}\pi \times (1.5{)}^3$

$=2.25\pi m^3$

From $\left(i\right)$

Volume of the rocket $=7.875\pi +1.5\pi +2.25\pi$

$=11.625\pi m^3$

$=36.521m^3$