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.

Answer 1

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 cm

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

 Height of the cylinder, h₁ = 18cm

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

Height of the cone, h₂ = 9 cm

now,

Total capacity of the tank= Volume of the cylinder + Volume of 2 cones

${\displaystyle \pi r^2{h}_1+2\times \frac{1}{3}\pi r^2{h}^2}$

${\displaystyle =\pi r^2(h_1+\frac{2}{3}{h}_2)}$

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

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

= 8316 cm³

Hence the total capacity of the tank is 8316 cm³.