Question

A boiler is in the form of a cylinder 2 m long with hemispherical ends each of 2 metre diameter. Find the volume of the boiler.

Answer 1

Given that:

Height of the cylinder h = 2 m

Radius of the cylinder and hemisphere are same and is given by

`r=d/2=2/2=1 m`

The volume of the cylinder is cylinder is

`V_1=pir^2h`

`=22/7xx1^2xx2`

`=22/7xx2 m^3`

There are two hemispheres at each ends of the cylinder, therefore the volume of the two hemispheres is

`V_2=2/3pir^3+2/3pir^3`

`=4/3xx22/7xx1^3`

`=22/7xx4/3m^2`

Therefore, the total volume of the boiler is given by

V = V₁ + V₂

`=(22/7xx2+22/7xx4/3) m^3`

`=22/7xx10/3m^3`

`=220/21 m^3`

Hence the volume of the boiler is `V =220/21 m^3`