What length of a solid cylinder $2 c m$ in diameter must be taken to recast into a hollow cylinder of length $16 c m$ , external diameter $20 c m$ and thickness $2.5 m m$ ?

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Solution

Let the length of the solid cylinder be $L$ .

$R =$ Radius of solid cylinder. $R_{e} a n d R_{i}$ are radii of hollow cylinder while L' is its length.

The volume of the solid cylinder = Volume of hollow cylinder

$π R^{2} L = π (R_{e}^{2} - R_{i}^{2}) L^{'}$

$L = \frac{(R_{e}^{2} - R_{i}^{2}) L^{'}}{R^{2}}$

$= \frac{(10^{2} - {9.75}^{2}) 16}{1^{2}} = 79 c m$

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