$A$ surveyor's $30$-$m$ steel tape is correct at some temperature. On a hot day,the tape has expanded to $30.01$ $m$. On that day,the tape indicates a distance of $15.52$ $m$ between two points. The true distance between these points is: (in $m$)

The volume of a metal sphere increases by $0.24\%$ when its temperature is raised by $40^{\circ}C$. The coefficient of linear expansion of the metal is .......... $^{\circ}C^{-1}$.

Draw the graph of the coefficient of volume expansion $(\alpha_V)$ versus temperature $(T)$ for a solid.

$A$ sheet of steel at $20^{\circ} C$ has dimensions as shown in the figure. If the coefficient of linear expansion for steel is $10^{-5} {^{\circ} C}^{-1}$, what is the change in the area at $60^{\circ} C$ (in $\text{ cm}^2$)?

Two metal rods $A$ and $B$ each of length $50 \ cm$ and diameter $4.0 \ mm$ are joined together at temperature $30^{\circ} C$. What is the change in length of the combined rod at $230^{\circ} C$ (in $mm$)? [Given linear expansion coefficients of rods $A$ and $B$ are respectively,$2.0 \times 10^{-5} /^{\circ} C$ and $1.0 \times 10^{-5} /^{\circ} C$]

When a cylinder is heated,its length increases by $2\%$. What is the percentage increase in its surface area (in $\%$)?