Newton's problem of finding the surface shape of a rotation body based on the condition of minimal resistance of the body when it moves in a rarefied medium is discussed. The problem is formulated in the form of a classical isoperimetric problem in calculus of variations. The exact solution is given in the class of piecewise differentiable functions. The numerical results of specific calculations of the functional for cone and hemisphere are presented. We prove that the optimization effect is significant by comparison of the results for cone and hemisphere with the value of the optimized functional for the optimal contour.