To make a conical funnel, its generatrix length is 20 cm, and its height should be () cm A. 2033B. 100C. 20D. 203
Let the height of cone be x, then the bottom radius is 202 − X2, and its volume is v = 13 π x (202-x2) (0 < x < 20), V ′ = 13 π (400-3x2). Let V ′ = 0, then the solution is X1 = 2033, X2 = - 2033 (rounding off). When 0 < x < 2033, V ′> 0; when 2033 < x < 20, V ′< 0; when x = 2033, V takes the maximum value