Hello, I'm on the last question on a math assignment here is the premise. 1. Take a circle of flat paper, cut out a sector with measure θ. 2. Roll this into a cone. 3. Find the optimum value of θ to get the maximum volume. I got this value as shown below. The final question: When the circle is cut there are two sectors so it is possible to make two cones. Find the value of values of x for which the sum of the volumes of the two cones is a maximum. Now I'm wondering how I can factor the fact that second sectors measure is 2π minus the first into my substitution of: Note: I'm assuming a slant height of 1 as the slant height does not matter when calculating the optimum angle. One other small question: I've done quite a bit of this working with mathematica but I'm following it and verifying it but I can't for the life of me see why there isn't another solution to the derivative as shown in the graph but not in the solution of the derivative.