The radius of a metal sphere at room temperature T is R, and the coefficient of linear expansion of the metal is α. The sphere is heated a little by a temperature ∆T so that its new temperature is T + ∆T. The increase in the volume of the sphere is approximately
1
2π R α Δ T
2
π R2 α ΔT
3
4π R3 α ΔT / 3
4
4π R3 α ΔT