Just as we created models for the Metrodome walls, we can postulate some
models for the shape of the Metrodome roof. For concreteness,
** for the remainder of the lab we will only use
the model that assumes that the walls are elliptical in shape**.

We will model the height of the Metrodome roof by the function

`roof := 1/3 - 1/6 * ((5*x/6)^2+y^2)^2;`

- Sketch this function
*restricted to the region inside the wall*. Hint: Maple will only graph this function over a square domain. Use level sets to figure out the restriction of the function to the interior of the ellipse. - Write down and solve a double integral for the volume of air underneath this model of the Metrodome roof.
- Do you think that the roof function is a good model for the real Metrodome roof? Support your assertion.

Thu Feb 20 09:21:36 CST 1997