Work done emptying a cylindrical tank

• Oct 2nd 2009, 02:46 PM
laura35066
Work done emptying a cylindrical tank
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.
• Oct 2nd 2009, 03:01 PM
galactus
$W=2\sqrt{(\frac{5}{2})^{2}-x^{2}}$

$W=\int_{-\frac{5}{2}}^{\frac{5}{2}}\left(\frac{7}{2}-x\right)(90)\left(2\sqrt{(\frac{5}{2})^{2}-x^{2}}\right)(10)dx$
• Oct 2nd 2009, 04:16 PM
laura35066
The first equation ...
I know that the formula for a circle is r^2 = (y-b)^2 + (x-a)^2 . Why are you squaring r twice?
• Oct 2nd 2009, 06:27 PM
skeeter
Quote:

Originally Posted by laura35066
I know that the formula for a circle is r^2 = (y-b)^2 + (x-a)^2 . Why are you squaring r twice?

consider it a typo ... it happens.
• Oct 3rd 2009, 01:59 AM
galactus
Yes, that is a typo. Thanks Skeeter.