SCalcET6 6.4.023.My Notes | . Question Par A tank is full of water. Find the wor

Question

SCalcET6 6.4.023.My Notes | . Question Par A tank is full of water. Find the work W required to pump the water out of the spout. Use the fact that water weighs 62.5 lb/ft3. (Use 3.14 for ?. If you enter your answer in scientific notation, round the decimal value to two decimal places. Use equivalent rounding if you do not enter your answer in scientific notation.) the tank is a cone except its point is sliced off forming a flat surface with radius=3. the radius of the top of the cone is radius=7.5 and the height of the cone is 8.

Explanation / Answer

Due to the nature of a cone, y varies linearly with x. When x = 0, y = 3 and when x = 8, y = 7.5, so the equation that relates x and y is: 1.7778x-y+3=0 The disk then has volume: dV = py^2 dx = p(1.7778x+3 )^2 dx. The weight of this disk is: dF = p dV = pp(1.7778x+3)^2 = 62.5p(1.7778x+3)^2. With the assumption that the spout is on top of the tank, a disk x meters up from the base has to travel the remaining 8 - x meters to get to the spout, so: dW = d dF = 62.5p(1.7778x+3)^2(8 - x). x varies from 0 to 8, so the required work is: W = ? 62.5p(1.7778x+3)^2(8 - x) dx (from x=0 to 8),

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