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A sphere and a cube made of the same material and having equal volume are heated to the same temperature and then left to cool in identical surroundings. Find the ratio of the amounts of radiation they initially emit (sphere: cube).

1. 1: 1
2. 4*pi/3: 1
3. (pi/6)^(1/3): 1
4. (1/2)(4*pi/3)^(2/3): 1

Correct answer: (pi/6)^(1/3): 1

Solution

At the same temperature, emitted radiation is proportional to surface area; for equal volumes the sphere has the smaller area, and the area ratio simplifies to (pi/6)^(1/3): 1.

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