Acircular hole in an aluminum plate is 3.231 cm in diameter at 0.000°c. what is its diameter when the temperature of the plate is raised to 64.91°c? the linear expansion coefficient of aluminum is 23.00 × 10-6 /c°.

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.

d = 3.236 cm

Thus, the diameter of the circular hole is 3.236 cm after heating at the given temperature.