Question

Theorem of Pappus: A torus is the object generated by revolving a circle about a line (the line should not pass through the circle but may be tangent to it). (a) Find the volume of the torus generated by revolving r?+ y =4 about the line r=5 . (b) A Different Approach: Let D be a closed bounded region in the plane with area A and centroid at 17.1). The volume generated by revolving D about the line L is given by V = distance traveled by the centroid X A = 21 X distance from centroid to L XA This result is known as the Theorem of Pappus. Verify your result in part (a) using the fact that the centroid of a circle is its center. (c) Compare the two methods used above to find the volume. In particular, under what conditions is one better/easier than the other? Which method is more intuitive?

Answer 1

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