设圆柱底面半径为R,高为H则S=2piRH+2piR^2 ==>H=S/(2piR)-RV=piR^2H=piR^2(S/(2piR)-R)=s/2R-piR^3V'(R)=S/2-3piR^2当V'(R)=0时,有Vmax==>R=根号(S/(6pi))因此 Vmax=S/3*根号(S/(6pi))