Chapter 14, Problem 48RE

(a)

To determine

To graph: The roof over the stage of an open air theater modeled by $f\left(x,y\right)=25\left[1+e^{-\frac{\left(x^2+y^2\right)}{1000}}{\cos }^2\left(\frac{\left(x^2+y^2\right)}{1000}\right)\right]$, where the stage is bounded by graphs of $y=\sqrt{{50}^2-x^2}$ and $y=0$ and is semicircular.

(b)

To determine

To calculate: The square foot of roofing required to cover the surface plotted in part (a) with the help of computer algebra system.