已知半径为R的球,问内接直圆柱的底半径r与高h为多少时,圆柱的体积为最大?

容易算出h=2(R^2-r^2)^0.5,故圆柱的体积V(r)=h*pai*r^2=2*pai*r^2*(R^2-r^2)^0.5,求导V'(r)=(4pai*R^2r-6pai*r^3)/(R^2-r^2)^0.5,令V'(r)=0.得r=(2/3)^0.5*R或r=0(舍去)所以当r=(2/3)^0.5*R,h=2*(1/3)^0.5*R,圆柱体...