Surfaces of Revolution Let S be the surface formed by ro
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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
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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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