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This is part of a long problem involving maximizing the size of a cone:
Basically, a circle of radius R has a sector of angle theta cut out of it. I found what the equation for the area of the sector would be: (pi/3)r^3(1-(theta/2pi))(1-(1-(theta/2pi)^2)^.5). The maximum angle is 1.840 radians.
The question now is how to maxamize the sum of the volume of the two cones created. One cone is of the sector removed, and the other is of the other sector. I thought the answer would be the original formula times 2, but this gives me the same answer.
Thoughts? Thanks!
Basically, a circle of radius R has a sector of angle theta cut out of it. I found what the equation for the area of the sector would be: (pi/3)r^3(1-(theta/2pi))(1-(1-(theta/2pi)^2)^.5). The maximum angle is 1.840 radians.
The question now is how to maxamize the sum of the volume of the two cones created. One cone is of the sector removed, and the other is of the other sector. I thought the answer would be the original formula times 2, but this gives me the same answer.
Thoughts? Thanks!