Question

A solid metallic cube having total surface area $24\,m ^{2}$ is uniformly heated. If its temperature is increased by $10^{\circ} C$, calculate the increase in volume of the cube $\left(\right.$ Given : $\left.\alpha=5.0 \times 10^{-4}{ }^{\circ} C ^{-1}\right)$

• A. $2.4 \times 10^{6} \,cm ^{3}$
• B. $1.2 \times 10^{5} \,cm ^{3}$
• C. $6.0 \times 10^{4}\, cm ^{3}$
• D. $4.8 \times 10^{5}\, cm ^{3}$

Answer 1

Answer: (B)

Increase in volume $\Delta V =\gamma V _{0} \Delta T$
$\gamma=3 \alpha$
So $\Delta V =(3 \alpha) V _{0} \Delta T$
Total surface area $=6 a ^{2}$,
where $a$ is side length $24=6 a ^{2} \,\,\, a =2 m$
Volume $V _{0}=(2)^{3}=8 m ^{3}$
$\Delta V =\left(3 \times 5 \times 10^{-4}\right)(8) \times 10 $
$=1.2 \times 10^{5} cm ^{3}$