设圆柱体的底面半径为R，高为H。那么，由勾股定理有：R²+(H/2)²=r²==> R²=r²-(H²/4)圆柱体的体积V=πR²H=π[r²-(H²/4)]H=π[r²H-(H³/4)]令V(H)=r²H-(H³/4)则，V'(H)=r²-(3/4)H²当V'(H)=0时，V有最大值此时：H=(2√3/3)r
