Work Done on Horizontal Tank pumping oil

[marc017]

Homework Statement

A gas station stores its gasoline in a tank underground. The tank is a cylinder lying horizontally on its side. The radius is 3 ft, the length is 14 ft, and the top of the tank is 10 feet under the ground. The density of gasoline is 42 lb/ft³

a) Consider a slice of gasoline that is Δy ft thick and located y ft above the center of the cylinder. Write an expression giving the work required to pump the slice out. Give your answer using the form below. (Use Deltay for Δy if necessary.)

Density · Volume of slice · Displacement of slice

The Attempt at a Solution

Density = 42 lb/ft³
Volume of Slice:

<br /> x^2 + y^2 = 3\\<br /> x = \sqrt{3-y^2}\\<br /> = 14\sqrt{3-y^2}\\<br /> <br /> \int 42(16-h)*14\sqrt{3-y^2}\,dy\\<br />
With the integral going from 0 to 6

Since I know my volume is wrong the integral can't be right, but for this sake, would the integral be right assuming the volume Is what I put?

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EDIT:

Would the volume for the slice be.
<br /> <br /> = 14\left( \sqrt{3-y^2} \right)^2dy\\<br />This would be so easy if they would let me stand the cylinder upright...

 

[SteamKing]

What's the equation for a circle with a radius of 3 feet?