16.25
MATHEMATICS - X
5. What length of a solid cylinder 2 cm in diameter must be taken to recast into a hot
cylinder of length 16 cm, external diameter 20 cm and thickness 2.5 mm?
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Given diameter of solid cylinder = 2 cm
Radius of solid cylinder, r = 1 cm
Volume of solid cylinder = πr2h
= π × 12 × h = πh → (1)
Length of hollow cylinder, H = 16 cm
External diameter = 20 cm
External radius = 10 cm
Thickness = 2.5 mm = 0.25 cm
Internal radius = 10 – 0.25 = 9.75 cm
Volume of hollow cylinder = π[102 – (9.75)2] × 16
= 16π × 19.75 × 0.25 → (2)
From (1) and (2), we get
Πh = 16π × 19.75 × 0.25
∴ h = 16 × 19.75 × 0.25 = 79 cm
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