Question

What length of a solid cylinder 2 cm in diameter must be taken to recast into a hollow cylinder of length 16 cm, external diameter 20 cm and thickness 2.5 mm?

Answer 1

The solid cylinder should be to hollow cylinder 

Given that, diameter of solid cylinder = 2 cm 

Length of hollow cylinder = 16 cm 

External diameter = 20 cm 

Thickness = 2.5 mm = 0.25 cm 

Volume of solid cylinder = πr²h ------(i) 

Radius of the cylinder = 1 cm 

So, volume of the solid cylinder = π(1)²h = π h 

Let length of the solid cylinder be h 

Volume of hollow cylinder = πh(R² – r²) 

Thickness = R – r 

⇒ r = 10 – 0.25 

⇒ Internal radius = 9.75 cm 

So, 

volume of hollow cylinder = π × 16(100 – 95.0625) 

= π × 16 × 4.9375 

≈ π × 16 × 4.94 -------(2) 

As we know that, 

volume of both solid and hollow cylinder must be the same, therefore 

π h = π × 16 × 4.94

⇒ h ≈ 79 cm 

∴ Length of the solid cylinder = 79 cm