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Two thin-walled spheres made of different materials are each filled with ice. One sphere has twice the radius and one-fourth the wall thickness of the other. The ice in the larger sphere melts completely in 25 minutes and that in the smaller sphere in 16 minutes. Find the ratio of the thermal conductivity of the larger sphere's material to that of the smaller sphere's material.

1. 4: 5
2. 25: 1
3. 1: 25
4. 8: 25

Correct answer: 8: 25

Solution

Since K is proportional to r*d/t, with the larger sphere having r doubled, d one-fourth, and t = 25 vs 16, the ratio works out to 8:25.

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