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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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$3 a^{3} α Δ T$

$4 a^{3} α Δ T$

$4 π a^{3} α Δ T$

$\frac{4}{3} π a^{3} α Δ T$

answer is B.

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Detailed Solution

$F r a c t i o n a l i n c r e a s e i n v o l u m e = \frac{Δ V}{V} = γ Δ T = 3 α Δ T$

$\Rightarrow Δ V = 3 a^{3} α Δ T$

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