# calculus problem I have tried 100 times

A tank in the shape of an inverted right circular cone has height 5 meters and radius 4 meters. It is filled with 2 meters of hot chocolate. Find the work required to empty the tank by pumping the hot chocolate over the top of the tank. The density of hot chocolate is δ=1080 kg/m3. Your answer MUST include the correct units.
I got :9.8*2592π∫(5h^2-h^3) (0,2) but it is incorrect and wanted to know how to get the correct answer.

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1. The radius of the surface of the chocolate at height y is 4y/5. So, the volume of a disc of thickness dy at height y from the tip of the cone is

v = π(4y/5)^2 dy

That makes the mass of the disc

m = 16π/25 y^2 dy * 1080 kg = 691.2πy^2 kg

The height that the mass must be raised to flow over the top is 5-y.

So, to empty the tank of chocolate at a depth of 2 meters, add up all the work for the discs

w = ∫[0,2] 691.2π*9.81y^2(5-y) dy

How did you come up with 2592?

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