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

We have,

Length of solid cylinder = L

Diameter o cylinder = 2 cm

Radius of cylinder = d/2 = 2/2 = 1cm

Volume of cylinder = πr²L ………… (i)

Length of hollow cylinder = 16 cm

External diameter = 20 cm

External radius = 20/2 = 10cm

Thickness = 2.5 mm = 0.25 cm

Inner radius = 10 – 0.25 = 9.75 cm

Volume = π (R² – r²) l …….. (ii)

From (i) and (ii)

πr²L = π (R² – r²) l

π × 1 × 1 × L = π × (10² – 9.75²) × 16

L = 79cm

∴ The length of the solid cylinder should be 79cm.