# Setting up the Integral

#### shamieh

##### Active member
All I need to do for this problem is set up the integral...Can someone tell me how to do that?

A tank has the shape of an inverted circular cone with height 10m and base with radius 1m. The tank is filled with water to a height of 8 m . Find the work required to empty the tank by pumping all of the water over the top.

NOTE: I just need to set up the integral, I don't actually have to calculate the problem.

Staff member

#### HallsofIvy

##### Well-known member
MHB Math Helper
All I need to do for this problem is set up the integral...Can someone tell me how to do that?

A tank has the shape of an inverted circular cone with height 10m and base with radius 1m. The tank is filled with water to a height of 8 m . Find the work required to empty the tank by pumping all of the water over the top.

NOTE: I just need to set up the integral, I don't actually have to calculate the problem.
From the side the cone looks like a triangle and we can use similar triangles. With height h, the distance from the center of the cone to the side, r, we have r/h= 1/10 so that r= h/10. The area of the disk at that height is $$\pi r^2= \pi h^2/100$$ and the volume of a thin 'layer of water', with thickness dh is $$\frac{\pi}{100}h^2 dh$$. Taking $$\delta$$ to be the density of water, it's weight is $$\frac{\pi\delta}{100}h^2dh$$. Lifting that from height h to height 10m requires $$\frac{\pi\delta}{100}h^2(10- h)dh$$ Joules of work. Integrate that from h= 0 to h= 8.