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 $^{\prime} \alpha^{\prime}$. The metal sheet is heated uniformly, by a small temperature $\Delta T$, so that its new temperature is $T +\Delta T$. Calculate the increase in the volume of the metal box.
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 $^{\prime} \alpha^{\prime}$. The metal sheet is heated uniformly, by a small temperature $\Delta T$, so that its new temperature is $T +\Delta T$. Calculate the increase in the volume of the metal box.
- [JEE MAIN 2021]
- A
$3 a^{3} \alpha \Delta T$
- B
$4 a ^{3} \alpha \Delta T$
- C
$4 \pi a ^{3} \alpha \Delta T$
- D
$\frac{4}{3} \pi a ^{3} \alpha \Delta T$
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