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.