Rectangular Soccer Field with 2 Semicircles at the End

Question

The rectangle has a straightaway each of 100 yards. There are 2 semi circles at each end. The distance around the whole track is 440 yards. What is the radius of each semicircle?

Answer 1

For the perimeter of the entire field, the straight edges of the straightaway comprise 100 yards + 100 yards = 200 yards. The two semi-circles can be thought of as just forming a circle of radius R. The circumference of this hypothetical circle is the remaining perimeter, of 440 yards - 200 yards = 240 yards.

C = 2πR, where C = 240 yards and R is the radius of the hypothetical circle.

R = C/(2π)

R = 240 yards/(2π) = 38.2 yards

This radius is the same as that for the two semi-circles.