Cut a sector with a central angle of a from a circular sheet of iron with radius r to make a funnel. When a is what, the volume of the funnel is the largest? High number, the function of the maximum and minimum application Answer a = 2pi radical (2 / 3)

Cut a sector with a central angle of a from a circular sheet of iron with radius r to make a funnel. When a is what, the volume of the funnel is the largest? High number, the function of the maximum and minimum application Answer a = 2pi radical (2 / 3)

Obviously, the generatrix of the funnel is equal to R, which is certain. Assuming that the center angle of the circle is a and the radius of the bottom is R1, then 2pi * R1 = 2 * pi * r * (A / (2pi)), the solution is R1 = a * r / (2pi), and the volume v = pi (a * r / (2pi)) ^ 2 * sqrt [(R) ^ 2 - (a * r / (2pi)) ^ 2) / 3, and the derivative is obtained and made equal to 0. The solution is a = 2 * pi * sqrt [2 / 3]