The temperature of a metal coin is increased by $100^{\circ} C$ and its diameter increases by $0.15 \%$. Its area increases by nearly (in $\%$)

Two rods $A$ and $B$ of identical dimensions are at temperature $30\,^{\circ}C$. If $A$ is heated up to $180\,^{\circ}C$ and $B$ up to $T\,^{\circ}C$,then the new lengths are the same. If the ratio of the coefficients of linear expansion of $A$ and $B$ is $4:3$,then the value of $T$ is........$^{\circ}C$.

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

Two rods,one of aluminum and another of steel,have initial lengths $l_1$ and $l_2$ respectively. They are joined together to form a single rod of length $(l_1 + l_2)$. If the coefficients of linear expansion for aluminum and steel are $\alpha_a$ and $\alpha_s$ respectively,and the increase in length for both rods is the same when the temperature of both is increased by $t \ ^\circ C$,then $\frac{l_1}{l_1 + l_2} = \dots$

Brass and lead rods of length $80 \ cm$ are connected in parallel at $0^{\circ}C$. If they are heated to $100^{\circ}C$,what will be the difference in length between their ends in $mm$? (Given: $\alpha_{brass} = 18 \times 10^{-6} \ ^{\circ}C^{-1}$ and $\alpha_{lead} = 28 \times 10^{-6} \ ^{\circ}C^{-1}$)

Three rods of equal lengths are joined to form an equilateral triangle $ABC$. $D$ is the mid-point of $AB$. The coefficient of linear expansion is $\alpha_1$ for the material of rod $AB$ and $\alpha_2$ for the material of rods $AC$ and $BC$. If the distance $DC$ remains constant for small changes in temperature,then: