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18. A cylinder with base radius r and height h is con- structed inside a sphere such that it is in contact with the surface of a sphere, as shown in the figー ure. The radius of the sphere is R- 11 in. (a) Create a polynomial expression for the vol- / >1 ume V of the cylinder in terms of h. (b) Make a plot of V versus h for 0 shs11 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 larg- est possible volume, and determine that volume.
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