The density of water at $20^oC$ is $0.998\  gm/cm^3$ and at $40^oC$ is $0.992\ gm/cm^3$. The mean coefficient of cubical expansion (in per ${}^oC$) is

A glass flask of volume $200 \,cm ^3$ is just filled with mercury at $20^{\circ} C$. The amount of mercury that will overflow when the temperature of the system is raised to $100^{\circ} C$ is ........ $cm ^3$ $\left(\gamma_{\text {glase }}=1.2 \times 10^{-5} / C ^{\circ}, \gamma_{\text {mercury }}=1.8 \times 10^{-4} / C^{\circ}\right)$

The volume of a metal sphere increases by $0.24\%$ when its temperature is raised by $40°C$. The coefficient of linear expansion of the metal is .......... $°C$

In cold countries, water pipes sometimes burst, because

If the volume of a block of metal changes by $0.12 \%$ when it is heated thrugh $20^oC$, the coefficient of linear expansion (in $^oC^{-1}$) of the metal is

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.