Each side of a box made


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 ' $\alpha$ '. The metal sheet is heated uniformly, by a small temperature $\Delta \mathrm{T}$, so that its new temperature is $\mathrm{T}+\Delta \mathrm{T}$. Calculate the increase in the volume of the metal box.

  1. $3 a^{3} \alpha \Delta T$

  2. $4 \mathrm{a}^{3} \alpha \Delta \mathrm{T}$

  3. $4 \pi a^{3} \alpha \Delta T$

  4. $\frac{4}{3} \pi \mathrm{a}^{3} \alpha \Delta \mathrm{T}$

Correct Option: 1


$\Delta \mathrm{V}=\mathrm{V} \gamma \Delta \mathrm{T}$

$\Delta \mathrm{V}=3 \mathrm{a}^{3} \alpha \Delta \mathrm{T}$

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