3. Using a Surface of Revolution. Imagine that the parabola given by * = 4py is revolved about the y-axis to form a dish of radius r (see figure below). This surface of revolution can be used as a model for a satellite receiving dish. If p = 5, then the parabola is * = 20y and has its vertex at the origin and focus at (0, 5). Part of the cost of construct- ing a receiving dish is related to surface area. Find the surface area of the dish formed by revolving a segment of the parabola x² = 20y about the y-axis to form a dish of radius r. The surface area is roughly proportional to the cube of what factor? 4. Comparing Answers. Use a graphing utility to find the surface area of the dish formed by revolving a segment of the parabola x² = 20y about the y-axis to form a dish of radius r. Compare the surface area you found in Exercise 3 to the graphing utility's value and verify that the answers are equivalent. If the answers are not equivalent, explain why they are different.

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