Question

A track-and-field coach wants two laps around the field to be 1000m. The physical education department needs a rectangular field that is as large as possible. Determine the dimensions of the track that will maximize the entire enclosed area. Do these dimensions meet the needs of the track coach and the physical education department? Explain.
(A diagram of a rectangular field with two semicircles at each end is shown, as well.)

Answer 1

Area = pi(r^2) + W^2. W=2r. The largest rectangular area is a square.

500 = 2pi(r) + 2(2r)
500 = 2r(pi + 2)
250/(pi + 2) = r

r= 48.623...

Width of the field :=: 97.256
The length of the field from top of circles :=: 194.492

If I havent missed anything that should do it :)

Answer 2

thanks for the help!