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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.
Solution
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`
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