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A long solid cylinder radiates power. It is recast into several smaller cylinders, each having the same length as the original and the same temperature. The total power radiated by all the pieces is twice that of the original cylinder. Ignoring radiation from the flat ends, how many smaller cylinders are formed?

1. 3
2. 4
3. 5
4. 6

Correct answer: 4

Solution

Conserving volume gives r = R/sqrt(n); each piece radiates proportional to r, so total power is n*(R/sqrt(n)) = sqrt(n)*R times the per-unit factor, and setting sqrt(n) = 2 gives n = 4.

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