# Thread: Swimming Pool -Double Integrals in Polar Coordinates-

1. ## Swimming Pool -Double Integrals in Polar Coordinates-

The problem says:

A swimming pool is circular with a 40-ft diameter. The depth is constant along east-west lines and increases linearly from 2ft at the south end to 7ft at the north end. Find the volume of water in the pool.

The approach I would think would be to see this as finding the volume under a plane with the bounds $\displaystyle 0\leq r\leq20$ and $\displaystyle 0\leq\theta\leq2\pi$

I'm having trouble finding the equation of this plane. I would think two points are (0,20,7) and (0,-20,2). However, I'm having trouble finding a third point. I know that from three points I can find two vectors, then a normal vector, and then the equation of the plane.

Thank you.

2. Originally Posted by Anthonny
The problem says:

A swimming pool is circular with a 40-ft diameter. The depth is constant along east-west lines and increases linearly from 2ft at the south end to 7ft at the north end. Find the volume of water in the pool.

...

I'm having trouble finding the equation of this plane. I would think two points are (0,20,7) and (0,-20,2).
However, I'm having trouble finding a third point. <---- (20, 0, 4.5)
I know that from three points I can find two vectors, then a normal vector, and then the equation of the plane.

Thank you.
...