One of the important question for the board exam class 10 from

mensuration chapter.This question is from r d sharma class 10 maths.

chapter-16.2 question number-12 maths r d sharma,mensuration.

In this question we have to find the volume of the boiler given that

a boiler which is in the form of a cylinder 2 m long with hemispherical

ends each of 2 m diameter.

Given,

Diameter of the hemisphere = 2 m

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

Height of the cylinder (h1) = 2 m

And, the volume of the Cylinder = Ï€r2h1 = V1

V1 = Ï€(1)22

V1 = 22/7 Ã— 2 = 44/7 m3

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

So, totally there are 2 hemispheres.

Then the volume of two hemispheres = 2 Ã— 2/3 Ã— 22/7 Ã— r3 = V2

V2 = 2 Ã— 2/3 Ã— 22/7 Ã— 13

V2 = 22/7 Ã— 4/3 = 88/21 m3

Thus,

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

V = V1 + V2

V = 44/7 + 88/21

V = 220/21 m3

Therefore, the volume of the boiler 220/21 m3