Question

A petrol tank is in the shape of a cylinder with hemispheres of same radius attached to both ends. If the total length of the tank is $6$m and the radius is $1$m, what is the capacity of the tank in litres.

Answer 1

Tank is in the shape of a cylinder with hemispheres of same radius attached to both ends.

Given : Length of the tank $=6m$

Radius $r=1m$ is same for all shapes

Height of hemispheres $=$ Radius $\left(r\right)=1m$

$\therefore$ Height of the cylinder $\left(h\right)=6-2=4m$

And radius of hemisphere $=1m$

Now, volume of the tank $=$ volume of two hemipheres $+$ volume of a cylinder

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

$=\pi (1{)}^2\times 4$

$=4\pi$

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

$=\frac{2}{3}\pi (1{)}^3$

$=\frac{2\pi }{3}$

$\therefore$ Volume of the tank $=2\times \frac{2\pi }{3}+4\pi$

$=\frac{16\pi }{3}$

$=16.75516m^3$

$=16577.16$ litres