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Each side of a box made of metal sheet in cubic shape is ‘a’ , 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 temperature is T+ΔT. Calculate the increase in the volume of the metal box.

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a

43πa3αΔT

b

3a3αΔT

c

4πa3αΔT

d

4a3αΔT

answer is B.

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Detailed Solution

Fractional increase in volume=ΔVV=γΔT=3αΔT⇒ΔV=3a3αΔT

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Each side of a box made of metal sheet in cubic shape is ‘a’ , 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 temperature is T+ΔT. Calculate the increase in the volume of the metal box.