What length of a solid cylinder 2 cm in diameter must be taken to recast into a hollow cylinder of length 16 cm,
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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