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# (Solved): 2. A cylindrical tank contains oil (use density as \rho in 3 lb ft ) . The radius of the tank is 3 ...

2. A cylindrical tank contains oil (use density as \rho in 3 lb ft ) . The radius of the tank is 3 feet, the length is 12 feet and oil enters and leaves the tank through an opening at the top. The tank is initially full of oil. Use the sketch below and complete each step below to find the work done in pumping all of the oil out of the opening at the top of the tank. You must use the axis provided. No calculators.(a) Find and expression for the volume of a single representative “slab” of oil that will move out of the tank. (b) Find the expression for the distance any single representative “slab” of oil must move to get out of the tank. (c) Find the expression for the force of a single representative “slab” of oil. (d) Set up (BUT DO NOT SOLVE), the Reimann sum that approximates the total work done in pumping all of the oil out of the tank. (e) Set up and solve the definite integral to find the total work done in pumping all of the oil out of the tank. Show your method(s) of evaluating the integral. Hint: You should split this into two integrals and notice one can be evaluated by interpreting it in terms of area as taught in 5.2. Keep exact values and attach the proper work unit in your final answer. 3. Use the same cylindrical tank as in problem 2. If the tank is initially full of oil, set up (BUT DO NOT SOLVE) the definite integral to find the work to pump oil out of the tank leaving a depth of 2 feet.

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