Work done emptying a cylindrical tank

**laura35066** · October 2nd 2009, 02:46 PM

I keep getting negative answers for this problem, so I was wondering if it can even be solved using the method taught in Calc. 1/2. We're supposed to first find volume, then force, when work, and then take the integral of the work.

A tank is in the shape of a cylinder lying on its side The cylinder is 10 feet long and 5 feet in diameter. It is filled with a liquid which has a density of 90 pounds per cubic foot. Find the work done emptying the tank through a spout that rises 1 foot above the top of the tank.

**galactus** · October 2nd 2009, 03:01 PM

$W=2\sqrt{(\frac{5}{2})^{2}-x^{2}}$

$W=\int_{-\frac{5}{2}}^{\frac{5}{2}}\left(\frac{7}{2}-x\right)(90)\left(2\sqrt{(\frac{5}{2})^{2}-x^{2}}\right)(10)dx$