(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A cylindrical gasoline tank with radius 4ft and length 15 ft is buried under a service station. The top of the tank is 10ft underground. Find the amount of work needed to pump all the gasoline in the tank to a nozzle 3 ft above the ground. Gasoline weighs 42lb/ft^3.

3. The attempt at a solution

So the way I have started is by setting a cylinder with the specified radius centered at (0,0). With that I know the top is at (0,4), bottom is at (0,-4) and the place it needs to reach is y = 17 (13ft above the top of the cylinder).

I divide the cylinder into strips of thickness delta y. So I know I need to find the weight of each of those strips and multiply it by the distance it must travel (17-y).

I have the density so I really now just need the volume of those strips. Volume = length * width * thickness. I have the thickness (delta y), the length (15), but I need the width.

I can't figure out how to find the width of the strips. I know that at y = 0 the width is 8 and at y=4 and y = -4 the width is 0.

Something like

[tex] width = 2\sqrt{16-y^2}[/tex]

would tell me the width with respect to y, but that would only be true from y=-4 to y=4, and it needs to stop after that.

Any advice would be appreciated thanks.

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# Homework Help: Work integrals

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