# Volume of liquid in a tank using a double integral

1. Mar 1, 2010

### mathmath

1. The problem statement, all variables and given/known data
The fluid level in the tank ((1/4)*(x-4)^2 + y^2 == 4) is 7 m on the left edge of the tank (where x=0) and 5 m on the right edge (where x=8). Find the equation of the plane of the liquid, and use a double integral to find the volume of liquid in the tank. [Hint: you should use a "dy dx" iterated integral, where the bounds on y depend on x, and are given by the equation of the base of the cylinder.]

2. Relevant equations
tank equation: (1/4)*(x-4)^2 + y^2 == 4

3. The attempt at a solution
I have found the equation of the plane of liquid to be: z=7 - 2 x/8, I am not sure if this is correct. I am confused on what the bounds would be for the double integral and what would be the integrand since the tank equation is set equal to a number.

Thanks!