Answer
The brass ring should be heated to a temperature of $74.6^{\circ}C$
Work Step by Step
We can find the required change in temperature of the brass ring so that the increase in radius $\Delta R$ is 0.0010 cm:
$\Delta R = \alpha~\Delta T~R$
$\Delta T = \frac{\Delta R}{\alpha~R}$
$\Delta T = \frac{0.0010~cm}{(19~\times 10^{-6}~K^{-1})(1.0000~m)}$
$\Delta T = 52.6~K$
$\Delta T = 52.6^{\circ}C$
The required increase in temperature is $52.6^{\circ}C$, so the brass ring should be heated to a temperature of $74.6^{\circ}C$
