# Homework Help: Area of an Athletic Field

1. Nov 24, 2007

### dmonlama

1. The problem statement, all variables and given/known data
An athletic field is to be built in the sahpe of a rectangle x units long capped by semicircular regions of radius r at the two ends. The field is to be bounded by a 400-m racetrack.
a. Express the area of the rectangular portion of the field as a funcion of x alone or r alone (your choice).
b. What values of x and r give the rectangular portion the largest possible area?

3. The attempt at a solution
For a, i expressed the equation in terms of r. I got 40000/pi - pi(r)^2. i just took the overall area and subtract it by the semicircular circles.

2. Nov 25, 2007

### HallsofIvy

What is your question? If you are asking if you did this correctly, I can't say because didn't show how you got that answer. Are you saying that the "overall area" is 4000/pi? How did you get that?

3. Nov 25, 2007

### dmonlama

i got the 40000/pi - pi(r)^2 by getting the overall area and minus it by the semicircular circles that cap the rectangular part. thats the answer for a.

4. Nov 25, 2007

### Dick

No, it's not. If r=0 that gives 40000/pi for the area, which can't be right. Again, show how you reached that conclusion.

5. Nov 26, 2007

### HallsofIvy

Now, please answer my original question. HOW did you get "the overall area"?