Each side of a cubic metal box is $a$ at room temperature $T$. The coefficient of linear expansion of the metal sheet is $\alpha$. The metal box 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.

• A
  $3 a^{3} \alpha \Delta T$
• B
  $4 a^{3} \alpha \Delta T$
• C
  $4 \pi a^{3} \alpha \Delta T$
• D
  $\frac{4}{3} \pi a^{3} \alpha \Delta T$