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1 9 4 Surface Area of Revolution Goal Given a curve find the area of the surface formed by rotating the curve about a horizontal or vertical axis Method Partition the appropriate interval then approximate the surface using frustrums of cones Area of a Cone Frustrum See derivation in the text pp548 549 Examples Find the area of the surface obtained by rotating the curve y x2 x 0 1 about the x axis Why not cylinders See http www math tamu edu dmanuel math152 frustrum pdf for a discussion of this 1 Find the area of the surface obtained by rotating the graph of y x2 0 x 1 about the x axis Method I Method II The circle x cos t y 1 sin t is rotated about the x axis Find the area of the resulting surface 2
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