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Unformatted text preview: , 2), (0 , 0), and (2 , 0). Find the centroid of the plate. You may use symmetry and known area or volume formulas from geometry to evaluate integrals. Math 166 Midterm Part II Page 3 3. (16 points) An upright water tank has a ﬂat base in the plane and is ﬁlled with water. The tank has height 7 feet, and, for 0 ≤ x ≤ 7, the crosssection parallel to the base at height x has area x 2 + 2. How much work is done in pumping all the water over the top edge of the tank? [Use δ lb / ft 3 for the weightdensity of water.] Math 166 Midterm Part II Page 4 4. (16 points) Let G be the portion of the graph with parametric equations x = 1 + sin t, y = 3 + 2 cos t, for 0 ≤ t ≤ 2 π . Set up, but do not evaluate, an integral for (a) the length of G . (b) the area of the surface generated by revolving G about the xaxis....
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 Spring '08
 Hotlz
 Math, Calculus, upright water tank

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