Cylinder in Sphere Volume Problem: The circle x2 + y2 = 25 is rotated about the y-axis
Chapter 12, Problem 13(choose chapter or problem)
Cylinder in Sphere Volume Problem: The circle x2 + y2 = 25 is rotated about the y-axis to form a sphere (Figure 12-3m). A cylinder is inscribed in the sphere, with its axis along the y-axis. Find an equation for the volume of the cylinder in terms of a sample point (x, y) in the first quadrant where the upper base of the cylinder touches the circle. Plot the volume of the cylinder as a function of x, and sketch the result. Find the value of x that gives the maximum volume, and find this maximum volume.
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