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 ΔT so that its new temperature is T + ΔT . The increase in the volume of the sphere is approximately

(a) 2πR α ΔT

(b) 2πR^{2} α ΔT

(c) (4πR^{3}α ΔT)/3

(d) 4πR^{3}α ΔT