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The Area of a Surface of Revolution The Surface of Revolution is the result when the graph of a continuous function is revolved about a line. If the graph were a horizontal line, the surface of revolution would simply be a cylinder: The lateral surface area of a cylinder is , where is the radius of the cylinder, and is the length of the line segment. Now consider a graph that has any amount of curvature: We use calculus to find this surface of revolution because the radius is not constant over the length of the object, and because finding the length of the curve requires calculus. 1

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Inferences about Two Proportions

The Area of a Surface of Revolution1

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The Area of a Surface of Revolution2

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