Suppose that a conical tank is obtained by rotating the line y = 2x for 0 ≤ x ≤ 3 about the y axis (with x and y measured in feet), and that the cone is filled with liquid weighting c pounds per cubic foot. Draw a picture of the situation, with appropriate labels. Find the work W required to empty the liquid out the top until there is a depth of 2 feet in the tank.

I'm studying for final but I can't remember how you do these kind of problems. I drew the graph and the cone but I'm not sure what I do next.

Question

Suppose that a conical tank is obtained by rotating the line y = 2x for 0 ≤ x ≤ 3 about the y axis (with x and y measured in feet), and that the cone is filled with liquid weighting c pounds per cubic foot. Draw a picture of the situation, with appropriate labels. Find the work W required to empty the liquid out the top until there is a depth of 2 feet in the tank.

I'm studying for final but I can't remember how you do these kind of problems. I drew the graph and the cone but I'm not sure what I do next.

anonymous · Answer

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anonymous · Answer

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Is it easier if I made the graph like this and solve it? integral from 2 to 3?