Building Design A new auditorium is built with a foundationin the shape of one-fourth of

Chapter 14, Problem 47

(choose chapter or problem)

Building Design  A new auditorium is built with a foundation in the shape of one-fourth of a circle of radius 50 feet. So, it forms a region R bounded by the graph of

\(x^2 +y^2 =50^2\)

with \(x\ \geq\ 0\) and \(y\ \geq\ 0\). The following equations are models for the floor and ceiling.

Floor: \(z=\frac{x+y}{5}\)

Ceiling: \(z = 20 + \frac{xy}{100}\)

(a) Calculate the volume of the room, which is needed to determine the heating and cooling requirements.

(b) Find the surface area of the ceiling.

Text Transcription:

x^2 +y^2 =50^2

x geq 0

y geq 0

z=x+y/5

z=20+xy/100