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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