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Question -

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



Answer -


Given,

Diameter of thehemisphere = 2 m

So, the radius of thehemisphere (r) = 1 m

Height of the cylinder(h1) = 2 m

And, the volume of theCylinder = πr2h= V1

V=π(1)22

V= 22/7× 2 = 44/7 m3

As at each of the endsof the cylinder, hemispheres are attached.

So, totally there are2 hemispheres.

Then the volume of twohemispheres = 2 × 2/3 × 22/7 × r3 = V2

V= 2× 2/3 × 22/7 × 13

V= 22/7× 4/3 = 88/21 m3

Thus,

The volume of theboiler (V) = volume of the cylindrical portion + volume of the two hemispheres

V = V+V2

V= 44/7 + 88/21

V = 220/21 m3

Therefore, the volumeof the boiler 220/21 m3

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