# Mov Maximum volume of a cone shaped cup

Sumit Oct 1, 2013 By:

**Reads:** 199

**Last modified:** 03 May 2013

Learn how find the largest possible volume of a cone-shaped up made from a circular piece of paper with radius R, where a sector has been removed and sides CA and CB are joined together. To complete this optimization problem, you'll need to draw a picture of the problem and write down what you know. Then you'll imagine that you'll take a vertical slice of the cone shaped cup so that you can use the pythagorean theorem to relate the radius of the paper to the radius and height of the cone. Solve the pythagorean theorem, the constraint equation, for one of the variables so that you can plug it into the optimization equation, which will be the equation for the volume of the cone. Then simplify the equation for the volume, take the derivative and set it equal to 0 to solve for the height. Plug the height back into the pythagorean theorem to find the radius, then plug both values back into the volume equation to find the volume.

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