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TAMU MATH 152 - 9_4

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1 9.4: Surface Area of RevolutionGoal: Given a curve, find the area of the surface formed by rotating the curve about a horizo ntal orvertical axis.Method: Partition the appropriate interval, then appr oximate the surface using fr ustrums 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 thex-axis.*-Why not cylinders? See http://www.math.tamu.edu/~dmanuel/math152/frustrum.pdf for a discus-sion of this.1Find 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


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TAMU MATH 152 - 9_4

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