Find the work required to empty the tank by pumping?

A tank in the shape of an inverted right circular cone has height 6m and radius 15m. It is filled to a depth of 3m with hot chocolate. Find the work required to empty the tank by pumping the hot chocolate over the top of the tank. Note: the density of hot chocolate is 1500 kg/m^3





i got the answer to be 7.95*10^7, but that's wrong

Find the work required to empty the tank by pumping?
I worked the problem and got: 8.48 x 10^6 N. I think you get this big amound because the radius is 15 meters. In fact, it's bigger than the height.





I worked it using the bottom of the circular cone as y=0 and the top of the cone y=6. The x-axes passing through the center of the cone.





I first calculated the volume of a slice:


Radius of slice = 7.5y,


therefore the Volume=Pi*(7.5y)^2*Δy = 56.25*Pi*y^2*Δy. Δy is the height of that slice.





Then we multiply the volume of the slice by the density of the hot chocolate to get the Force. I got: 84375*Pi*y^2*Δy kilograms.





Since W=Force * distance, distance to move is (6-y) meters, then


(84375*Pi*y^2*Δy) * (6-y), Integrate that from 0 to 3 and we get approximately:


8.48 x 10^6 J

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