1 A cone-shaped drinking cup is made from a circular piece of paper with radius R by cutting out a “sector” and joining the edges CA and CB. Set up a function representing the volume of the drinking cup as a function of one variable only. Then, use calculus to determine the dimensions of the drinking cup that yield the greatest volume. Be sure to verify that your answer corresponds to a maximum. Determining the an expression for the radius of the new circular cone in addition to an expression for the height of the cone will be critical in answering the question. Note, the size of the sector that can be removed is not fixed. As its size changes, so does the angle theta and so does the resulting radius and height of the cone that is formed by bringing the edges CA and CB together.
(Hint, to better see the geometry pertaining to the problem, draw a large circle on a piece of paper and cut out a sector. )
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