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A metal sphere of radius R at temperature T has linear expansion coefficient alpha. When heated by a small amount delta-T, find the approximate increase in its volume.

1. 2 pi R alpha (delta-T)
2. pi R² alpha (delta-T)
3. 4 pi R³ alpha (delta-T) / 3
4. 4 pi R³ alpha (delta-T)

Correct answer: 4 pi R³ alpha (delta-T)

Solution

Using gamma = 3 alpha and V = (4/3) pi R³, delta-V = 3 alpha * (4/3) pi R³ * delta-T = 4 pi R³ alpha delta-T.

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