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

The volume of a metal sphere increases by $0.30 \%$,when its temperature is raised by $50^{\circ} C$. The coefficient of linear expansion of the metal is

The length of a metal rod at $30^{\circ} C$ is $30 \ cm$. If its temperature is raised to $105^{\circ} C$, its length is increased by $0.027 \ cm$. Then the coefficient of linear expansion of the metal is

At what temperature (in $ ^{\circ} C$) should a gold ring of diameter $6.230 \,cm$ be heated so that it can be fitted on a wooden bangle of diameter $6.241 \,cm$ (in $.7$)? Both diameters were measured at room temperature $(27^{\circ} C)$. (Given: coefficient of linear thermal expansion of gold $\alpha_{L}=1.4 \times 10^{-5} \,K ^{-1}$)

$A$ blacksmith fixes a circular iron frame on the wooden wheel of a bullock cart. The diameters of the wooden wheel and the circular iron frame are $5.012 \ m$ and $5 \ m$ respectively at $27^{\circ} C$. The temperature (in $^{\circ} C$) to which the iron ring must be heated so as to fit the wooden wheel is (Coefficient of linear expansion of iron $= 1.2 \times 10^{-5} \ ^{\circ} C^{-1}$).

An aluminium and steel rod having same lengths and cross-sections are joined to make a total length of $120 \ cm$ at $30^{\circ} C$. The coefficients of linear expansion of aluminium and steel are $24 \times 10^{-6} /{ }^{\circ} C$ and $1.2 \times 10^{-5} /{ }^{\circ} C$, respectively. The length of this composite rod when its temperature is raised to $100^{\circ} C$, is . . . . . . $cm$. (in $cm$)