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 1

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 = πr²h₁ = V₁

V₁ = π(1)²2

V₁ = 22/7 × 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 × 2/3 × 22/7 × r³ = V₂

V₂ = 2 × 2/3 × 22/7 × 1³

V₂ = 22/7 × 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.