Cylinder in Sphere Problem: A cylinder is to be inscribed in a sphere of radius 10 cm
Chapter 8, Problem 25(choose chapter or problem)
Cylinder in Sphere Problem: A cylinder is to be inscribed in a sphere of radius 10 cm (Figure 8-3x). The bottom and top bases of the cylinder are to touch the surface of the sphere. The volume of the cylinder will depend on whether it is tall and narrow or short and wide. Figure 8-3x a. Let (x, y) be the coordinates of a point on the circle, as shown. Write an equation for the volume of the cylinder in terms of x and y. b. What radius and height of the cylinder will give it the maximum volume? What is this volume? Justify your answer. c. How are the radius and height of the maximum-volume cylinder related to each other? How is the maximum cylinder volume related to the volume of the sphere?
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