已知r^2*h=V/π（r和h为未知量）,当r和h各为多少时,r^2+rh有最小值?

Question

已知r^2*h=V/ π（r和h为未知量）,当r和h各为多少时,r^2+rh有最小值?

Answer 1

均值不等式,A^2+B^2>=2AB,取等条件为A=B.
故当 r^2=rh,即 r=h=(V/π)^(1/3) 时,r^2+rh有最小值2(V/π)^(2/3).