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

8-33.

diagramAn indoor physical fitness room consists of a rectangular region with a semicircle on each end. The perimeter of the room is to be a -meter running track. Let be the area of the rectangular region. Label all parts of the diagram. Note that is the radius of the circular portion. Homework Help ✎

  1. Write an equation for in terms of .

    circumference (or in this case)

  2. Express A as a function of .

    Use the information from part (a).

  3. 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.