Calc07_4worksheet

# Calc07_4worksheet - x-axis Check your result with a formula from geometry 6 The surface of an astroid Find the area of the surface generated by

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A.P Calculus Worksheet: Areas of Surfaces of Revolution Find the areas of the surfaces generated by revolving the curves in problems 1-4 about the axes indicated: 1. / 2, 0 4 y x x = , about the x -axis. Check your result with a formula from geometry. 2. 3 , 0 2 9 x y x = , about the x -axis. 3. 2 2 , 0 2 y x x x = - , about the x -axis. 4. 3 , 0 1 3 y x y = , about the y -axis. - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 5 . The surface of a sphere . Use an integral to find the surface area of the sphere generated by revolving the semicircle 2 1 y x = - , 1 1 x - ≤ , about the
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Unformatted text preview: x-axis. Check your result with a formula from geometry. 6. The surface of an astroid . Find the area of the surface generated by revolving the portion of the astroid 2/3 2/3 1 x y + = shown below about the x-axis. ( Hint : Revolve the first quadrant portion ( 29 3/ 2 2/3 1 y x =-, 1 x ≤ ≤ , about the x-axis, and double your result.) - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -Answers: 1. 4 5 π 2. 98 81 3. 4 4. ( 29 2 2 1 9-5. 4 6. 12 5 2 2 3 3 1 x y + =...
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## This note was uploaded on 02/12/2011 for the course MAC 2233 taught by Professor Smith during the Spring '08 term at University of Florida.

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