Answer
The required increase in temperature would be $587~K$
Work Step by Step
We can find the required change in temperature of the aluminum so that the increase in circumference is 26 cm:
$\Delta L = \alpha~\Delta T~L$
$\Delta T = \frac{\Delta L}{\alpha~L}$
$\Delta T = \frac{0.26~m}{(25~\times 10^{-6}~K^{-1})(17.72~m)}$
$\Delta T = 587~K$
The required increase in temperature would be $587~K$.
