### Home > PC3 > Chapter Ch8 > Lesson 8.1.2 > Problem 8-33

8-33.

An indoor physical fitness room consists of a rectangular region with a semicircle on each end. The perimeter of the room is to be a be the area of the rectangular region. Label all parts of the diagram. Note that

*is the radius of the circular portion.*

Write an equation for

in terms of.circumference

(or in this case) Express

as a function of.Use the information from part (a).

What

*diameter*will create a maximum area for the physical fitness room?Graph your function from part (b) on a calculator. Locate the point that represents a maximum.