Answer
The brass plate should be heated to a temperature of $26.75^{\circ}C$
Work Step by Step
We can find the required change in area of the hole:
$\Delta A = 4.91000~cm^2-4.90874~cm^2 = 0.00126~cm^2$
We can find the required change in temperature of the brass plate so that the increase in area of the hole $\Delta A$ is $0.00126~cm^2$:
$\Delta A = 2~\alpha~\Delta T~A$
$\Delta T = \frac{\Delta A}{2~\alpha~A}$
$\Delta T = \frac{0.00126~cm^2}{(2)(19~\times 10^{-6}~K^{-1})(4.90874~cm^2)}$
$\Delta T = 6.75~K$
$\Delta T = 6.75^{\circ}C$
The required increase in temperature is $6.75^{\circ}C$, so the brass plate should be heated to a temperature of $26.75^{\circ}C$
