Answer:
A1 = π R^2 original area
A2 = π (R + ΔR)^2 area of hole increased in radius by ΔR
A2 - A1 = π (2 R ΔR + ΔR^2) change in area due to heating
Δ A = π 2 R ΔR ΔR^2 is small and will be omitted
ΔR = R c ΔT where ΔT is the temperature change
Thus the coefficient of area expansion is twice that of the coefficient of linear expansion