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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?
Solution
Here, r = Internal radius
R = External radius = 10 cm
h = Length of the cylinder
t = Thickness = 0.25 cm
Volume of the hollow cylinder = πh(R2 - r2) = π (16) (102 - (10-0.25)2) = 79 π cm3
Volume of the solid cylinder = Volume of the hollow cylinder
We know that the radius of the solid cylinder is 1 cm.
∴ π(12)h = 79 π
h = 79 cm
Hence, length of the solid cylinder that gives the same volume as the hollow cylinder is 79 cm.
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