A boiler is in the form of a cylinder $ 2 \mathrm{~m} $ long with hemispherical ends each of 2 metre diameter. Find the volume of the boiler.

Given:

A boiler is in the form of a cylinder \( 2 \mathrm{~m} \) long with hemispherical ends each of 2 metre diameter. 

To do:

We have to find the volume of the boiler.

Solution:

Diameter of the cylinder $= 2\ m$

This implies,

Radius of the cylinder $r = \frac{2}{2}$

$= 1\ m$

Length of the cylindrical part $h = 2\ m$

Therefore,

Volume of the boiler $=2 \times \frac{2}{3} \pi r^{3}+\pi r^{2} h$

$=\frac{4}{3} \pi r^{3}+\pi r^{2} h$

$=\pi r^{2}(\frac{4}{3} r+h)$

$=\frac{22}{7}(1)^{2}(\frac{4}{3} \times 1+2)$

$=\frac{22}{7}(\frac{4}{3}+2)$

$=\frac{22}{7} \times \frac{4+6}{3}$

$=\frac{22}{7} \times \frac{10}{3}$

$=\frac{220}{21} \mathrm{~m}^{3}$

The volume of the boiler is $\frac{220}{21}\ m^3$.

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Updated on: 10-Oct-2022

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