The conical tank shown here is filled with olive oil weighing 47 lb/ft

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The conical tank shown here is filled with olive oil weighing 47 lb/ft3. How much work does it take to pump all of the oil to the rim of the tank?

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The conical tank shown here is filled with olive oil weighing 47 lb/ft3. How much work does it take to pump all of the oil to the rim of the tank?

Explanation & Steps

Step 1: Firstly, assume that the oil is separated into thin slabs, with a slab located at a distance 'y' (from the cone's bottom) and a thickness of $\Delta y$ .

Step 2: Using the slab's area and thickness, calculate the volume of the oil slab under consideration.

Step 3: Using weight per unit volume and volume, determine the force F(y) needed to raise the oil slab under consideration.

Step 4: By multiplying force by distance, one can find the amount of work needed to raise the slab to the cone's rim.

Step 5: Integrating the work inside the interval [0, 10] allows for the computation of the total work completed because the number of oil slabs, n goes to infinity.