18. A cylinder with base radius r and height h is constructed inside a sphere such that...
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18. A cylinder with base radius r and height h is constructed inside a sphere such that it is in contact with the surface of a sphere, as shown in the figure.
The radius of the sphere is in.
(a) Create a polynomial expression for the volume V of the cylinder in terms of h.
(b) Make a plot of V versus h for in.
(c) Using the roots command determine h if the volume of the cylinder is 2,000 in.3.
(d) Determine the value of h that corresponds to the cylinder with the largest possible volume, and determine that volume.
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