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. a Find the distance around the track along its inner edge.

Answer 1

We are essentially asked to find the inner perimeter of the track. We already know the length of the inner parallel lines of the track, which has been stated to be 100 m. What we need to solve for now is the circumference of the semicircles that make up the ends of the inside of the track. Since there are two semicircles, these combine to form one full circle so we can use the formula to find the circumference of the circle with a diameter of 60 m, which was given to us. With a diameter of 60m, the radius will be 30m. Now we can solve this problem.

C = 2πr
C = 2π(30)
C = 60π

The semicircle ends of the track are a distance of 60π m, and now we simply add the lengths of the inner track which are 100 m each. Therefore, the total distance of the inner track is:

P = 60π + 100m + 100m
P = 200 + 60π
P = 388.5 m