Try it on paper first. A hint, the key idea and the worked solution are here when you need them.
A running track has two straight sides of each and two semicircular ends. The inner edge has ends of radius , and the track is wide. Find the length of the outer edge, the area of the track and the length of the inner edge. Take .
A window is a rectangle plus a semicircle. The inner edge of a track is and each lane further out is longer by . Three touching circles of radius enclose .
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Given. , , , so the outer radius is .
Step 1. The outer edge. .
Step 2. The inner edge. .
Step 3. The straight strips. .
Step 4. The ring. .
Step 5. The area of the track. .
Answer: the outer edge is , the inner edge is , and the track has an area of .
Check. The outer edge minus the inner edge is , which is .
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