Question

The drawing below (not to scale) shows a running track. The ends are semicircles. The distance between the two inner parallel straight lines is 60 meters, and they are each 100 meters long. The track is 10 meters wide. Find the area of the actual track (the shaded region).

Answer 1

700pi+2000. First calculate the area of the two straight shaded region. Each of them is 10 m wide and 100 m long, so their total area is 2*10*100=2000 m^2. Then calculate the curved regions, each of which is equal to the area of the bigger half circle minus small half circle, which is 1/2*pi*[(60+10+10)/2]^2-1/2*pi*(60/2)^2=350 pi m^2, so the total area is 2*350pi+2000 m^2=700pi+2000.