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

Given,

Diameter of the solid cylinder = 2 cm

Length of hollow cylinder = 16 cm

The solid cylinder is recast into a hollow cylinder of length 16 cm, external diameter of 20 cm and thickness of 2.5 mm = 0.25 cm

We know that,

Volume of a cylinder = πr²h

Radius of the solid cylinder = 1 cm

So,

Volume of the solid cylinder = π1²h = πh cm³

Let’s assume the length of the solid cylinder as h

And,

Volume of the hollow cylinder = πh(R²– r²)

Thickness of the cylinder = (R – r)

0.25 = 10 – r

So, the internal radius of the cylinder is 9.75 cm

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

Hence, it’s understood that

Volume of the solid cylinder = volume of the hollow cylinder

πh = π × 16(100 – 95.06)

h = 79.04 cm

Therefore, the length of the solid cylinder is 79.04 cm.