Q. 53.8( 13 Votes )

# 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?

The solid cylinder should be to hollow cylinder

Given that, diameter of solid cylinder = 2 cm

Length of hollow cylinder = 16cm

External diameter = 20cm

Thickness = 2.5mm=0.25cm

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

Radius of the cylinder = 1cm

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 = 9.75cm

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 ≈ 79cm

Length of the solid cylinder = 79cm

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