Surfaces of Revolution Let S be the surface formed by rotating the region under the
Chapter 16, Problem 42(choose chapter or problem)
Surfaces of Revolution Let S be the surface formed by rotating the region under the graph z = g(y) in the yz-plane for c y d about the z-axis, where c 0 (Figure 23). (a) Show that the circle generated by rotating a point (0,a,b) about the z-axis is parametrized by (a cos ,a sin , b), 0 2 (b) Show that S is parametrized by G(y,) = (y cos ,y sin , g(y)) 13 for c y d, 0 2. (c) Use Eq. (13) to prove the formula Area(S) = 2 d c y 1 + g (y)2 dy
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