A tank full of cooking oil has the shape of a paraboloid obtained by rotating a parabola about the vertical axis, such that the tank height is 4 m and the radius at its top is 4 m. a. How much work is required to empty the tank through an 2-m-high outlet pipe  at the top of the tank? (The density of the oil is 920 kg/m3 .)   b. When a 4,000,000 J of work is done, what is the depth of oil remaining in the tank?

Question

A tank full of cooking oil has the shape of a paraboloid obtained by rotating a parabola about the vertical axis, such that the tank height is 4 m and the radius at its top is 4 m.

a. How much work is required to empty the tank through an 2-m-high outlet pipe  at the top of the tank? (The density of the oil is 920 kg/m3 .)  

b. When a 4,000,000 J of work is done, what is the depth of oil remaining in the tank?

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