The roof over the stage of an open air theater at a theme

Chapter 14, Problem 46

(choose chapter or problem)

The roof over the stage of an open-air theater at a theme park is modeled by

\(f(x, y)=25\left[1+e^{-\left(x^{2}+y^{2}\right) / 1000} \cos ^{2}\left(\frac{x^{2}+y^{2}}{1000}\right)\right]\)

where the stage is a semicircle bounded by the graphs of \(y=\sqrt{50^{2}-x^{2}}\) and y = 0.

(a) Use a computer algebra system to graph the surface.

(b) Use a computer algebra system to approximate the number of square feet of roofing required to cover the surface.

Text Transcription:

f(x, y) = 25 [1 + e^{-(x^2 + y^2) / 1000} cos^2 (x^2 + y^2 / 1000)]

y = sqrt{50^2 - x^2}