 # A petrol tank is a cylinder of base diameter 21 cm and length 18 cm Question:

A petrol tank is a cylinder of base diameter 21 cm and length 18 cm fitted with conical ends each of axis length 9 cm. Determine the capacity of the tank.

Solution:

To find the total capacity of the tank, we have to add the volume of the cylinder and cone.

Diameter of the cylinder, $d=21 \mathrm{~cm}$

Radius of the cylinder, $r=\frac{d}{2}=\frac{21}{2} \mathrm{~cm}$

Height of the cylinder, $h_{1}=18 \mathrm{~cm}$

Also, radius of cone, $r=\frac{21}{2} \mathrm{~cm}$

Also, radius of cone, $r=\frac{21}{2} \mathrm{~cm}$

Height of the cone, $h_{2}=9 \mathrm{~cm}$

Now,

Total capacity of the tank

= Volume of the cylinder + Volume of 2 cones

$=\pi r^{2} h_{1}+2 \times \frac{1}{3} \pi r^{2} h_{2}$

$=\pi r^{2}\left(h_{1}+\frac{2}{3} h_{2}\right)$

$=\frac{22}{7} \times\left(\frac{21}{2}\right)^{2} \times\left(18+\frac{2}{3} \times 9\right)$

$=\frac{22}{7} \times\left(\frac{21}{2}\right)^{2} \times 24$

$=8316 \mathrm{~cm}^{3}$

Hence the total capacity of the tank is $8316 \mathrm{~cm}^{3}$.