What length of solid cylinder $2 cm$ in diameter must be taken to recast into a hollow cylinder of external diameter $20 cm$, $0.25 cm$ thick and $15 cm$ long?

Using the principle of volume conservation, the volume of the solid cylinder equals the volume of the hollow cylinder, given by pi * 1^2 * L = pi * (10^2 - 9.75^2) * 15. Solving for the length L gives L = (100 - 95.0625) * 15. This calculates to a required length of 74.06 cm.

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