Answer:
3.236 cm
Explanation:
diameter at 0°C, do = 3.231 cm
Initial temperature, To = 0° C
Final temperature, T = 64.91° C
ΔT = T - To = 64.91
Coefficient of linear expansion, α = 23 x 10^-6 / °C
Let d be the diameter when the temperature is raised.
Coefficient of areal expansion = 2 x α = 46 x 10^-6 / °C
Use the formula for the areal expansion
A = Ao(1 + βΔT)
where, ΔT be the rise in temperature.
[tex]\frac{\pi d^{2}}{4}=\frac{\pi d_{0}^{2}}{4}\left ( 1+\beta \Delta T \right )[/tex]
[tex]d^{2}=d_{0}^{2}\left ( 1+\beta \Delta T \right )[/tex]
[tex]d^{2}=3.231^{2}\left ( 1+46\times10^{-6}\times 64.91\right )[/tex]
[tex]d^{2}=10.44\left ( 1.00298\right )=10.471[/tex]
d = 3.236 cm
Thus, the diameter of the circular hole is 3.236 cm after heating at the given temperature.
