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# hw6 - 1 By revolving the curve y = x 2 3 with 0 ≤ x ≤ 8...

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Fall 2010, MAT21B, Written Homework 6 Due: Wednesday, May 12 lecture time in class Name Student ID Section number TA’s name Instructions. You are required to complete and hand in all three problems. One of these three problems will be randomly picked and graded by our TAs. The homework has totally 10 points. If you turned in a ”reasonable (as determined by the TA)” homework showing your hard work, you will automatically get 4 points. The rest 6 points comes from the one problem graded by our TAs. PLEASE clearly write down your NAME, Student ID, SECTION number as well as your TA’s name. Otherwise, your homework will be easily got lost due to the size of the class.
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Unformatted text preview: 1. By revolving the curve y = x 2 / 3 with 0 ≤ x ≤ 8 ft along the y-axis, we get a tank. Suppose this tank is ﬁlled with seawater whose weight-density is 64 lb/ft 3 . How much work does it take to pump the liquid to the level of the top of the tank? 2. A circular plate with diameter 4ft is submerged vertically in a swimming pool. The distance from the top of the plate to the water surface is 3 ft. Find the force exerted by the water against one side of the disk. (Water’s weight-density is 62.4 lb/ft 3 ). 3. Evaluate the integral Z 8 1 log 8 x x dx 1...
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