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Each side of a box made of metal sheet in cubic shape is 'a' at room temperature 'T', the coefficient of linear expansion of the metal sheet is 'α'. The metal sheet is heated uniformly, by a small temperature ΔT, so that its new temperature is T + ΔT. Calculate the increase in the volume of the metal box.

1. 3a³αΔT
2. 4a³αΔT
3. 4πa³αΔT
4. (4/3)πa³αΔT

Correct answer: 3a³αΔT

Solution

The increase in volume of a cubic box due to thermal expansion can be calculated using the formula for volume expansion, which is based on the linear expansion coefficient. Since the box has three dimensions, the total increase in volume is three times the linear expansion, leading to the result of 3a³αΔT.

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