WS2 - Math 152 Workshop 2 Spring 2011 1 Let R be the...

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Math 152 Workshop 2 Spring 2011 1. Let R be the parabolic region in the x - y plane bounded below by the curve y = x 2 and above by the line y = 1. (a) Sketch R . Set up and evaluate an integral that gives the area of R . (b) Suppose a solid has base R and the cross-sections of the solid perpendicular to the y -axis are squares. Sketch the solid and find its volume. (c) Suppose a solid has base R and the cross-sections of the solid perpendicular to the y -axis are equilateral triangles. Sketch the solid and find its volume. 2. Start with the region A in the first quadrant enclosed by the x -axis and the parabola y = 2 x (2 - x ). Then obtain solids of revolution S 1 , S 2 , and S 3 by revolving A about the lines y = 4 , y = - 2 , and x = 4 respectively. All three solids are (unusual) “doughnuts” which are 8 units across, whose hole is 4 units across, and whose height is 2 units. Sketch them. (a) Which do you expect to have larger volume, S 1 or S 2 ? Compute their volumes exactly and check your guess.
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