Question

A petrol tank is a cylinder of base diameter 21cm and length 8cm fitted with conical ends each of axis length 9 cm. Determine the capacity of the tank

Answer 1

the capacity of the tank is 174636

Answer 2

Given :-

Base diameter of the petrol tank = 21 cm

Height of the cylinder = 8 cm

Height of cone = 9 cm

To Find :-

The capacity of the tank.

Analysis :-

In order to find the total capacity of the tank, first find the volume of the cylinder and the 2 cones.

Add the volume of the cylinder and the 2 cones to get the total capacity of the tank.

Solution :-

We know that,

• d = Diameter
• r = Radius
• h = Height

Given that,

Diameter of the cylinder = 21 cm

By the formula,

$\underline{\boxed{\sf Radius=\dfrac{Diameter}{2} }}$

Substituting them,

$\sf Radius=\dfrac{21}{2}$

Given,

Height of the cylinder (h₁) = 18 cm

Radius of the cone = 21/2

Height of the cone (h₂) = 9 cm

We know,

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

$\underline{\boxed{\sf \pi r^{2} h_1 + 2 \times \dfrac{1}{3} \pi r^{2} h^{2}}}$

$\sf =\pi r^{2} \bigg( h_1+\dfrac{2}{3} h_2 \bigg)$

$\sf =\dfrac{22}{7} \times \bigg(\dfrac{21}{2} \bigg)^{2} \times \bigg( 18+\dfrac{2}{3} \times 9 \bigg)$

$\sf =\dfrac{22}{7} \times \bigg( \dfrac{21}{2} \bigg)^{2} \times 24$

$\sf =8316 \ cm^{3}$

Therefore, total capacity of the tank is 8316 cm³