The conical tank shown here is filled with olive oil weighing 41 lb/ft^3. How much work does it take to pump all of the oil to the rim of the tank? W = ft-lb (Round to the nearest whole number as needed.)

The conical tank shown here is filled with olive oil weighing 41 lb/ft^3. How much work does it take to pump all of the oil to the rim of the tank? W = ft-lb (Round to the nearest whole number as needed.)

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The conical tank shown here is filled with olive oil weighing 41 lb/ft^3. How much work does it take to pump all of the oil to the rim of the tank? W = ft-lb (Round to the nearest whole number as needed.)

Explanation & Steps

Step (1): First of all consider the oil is divided into different into thin slabs and a slab is situated at distance ‘y’ (from bottom of the cone) of thickness \Delta y.

Step (2): Determine the volume of the considered oil slab using area and thickness of this slab.

Step (3): The force F(y) required to lift the considered oil slab using weight per unit volume and volume.

Step (4): The work required to lift the slab upto the rim of cone can be determined by multiplying force with distance.

Step (5): Since number of oil slabs ‘n’ tends to infinity, total work done can be calculated by integrating the work in the interval [0, 20].

Detailed Answer

Answer
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