MAT 21B Midterm: MATH 21B Midterm Exam 2 Winter 2010 Solutions
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MAT 21B Full Course Notes
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1 (25 points) the region bounded between the x-axis and the curve y = 1 x2 is revolved around the line y = 1. Compute the volume of the resulting solid. (note that the solid has a hole . ) This is a solid of revolution of washer type, with outer radius. R(x) = (1 x2) ( 1) = 2 x2, and inner radius r(x) = 0 ( 1) = 1. The range for the x-coordinate is found by inter- secting the curve y = 1 x2 with the x-axis y = 0, which gives x = 1, +1. (cid:2)(2 x2)2 12(cid:3) dx = z 1. 2 (25 points) a bucket weighing 10 pounds is pulled up to the roof of a 30-foot high building using a rope and pulley. The rope itself has a weight density of. Compute the amount of work that is required, in lb-ft units.
