An ellipsoid is formed by rotating the ellipse x2 + 4y2 = 16 about the y-axis. A

Chapter 12, Problem T.14

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An ellipsoid is formed by rotating the ellipse x2 + 4y2 = 16 about the y-axis. A cylinder is inscribed in the ellipsoid with its axis along the y-axis and its two bases touching the ellipsoid (Figure 12-7h). Plot the graph of the volume of the cylinder as a function of its radius, x. Find numerically the radius and altitude of the cylinder of maximum volume, and approximate the value of this maximum volume.

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