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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