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Try this beautiful problem from AMC-8-2014 (Geometry) based on Circumference of a Semicircle

On A straight one-mile stretch of highway, 40 feet wide, is closed. Robert rides his bike on a path composed of semicircles as shown. If he rides at 5miles per hour, how many hours will it take to cover the one-mile stretch?

- \(\frac{\pi}{11}\)
- \(\frac{\pi}{10}\)
- \(\frac{\pi}{5}\)

Geometry

Semicircle

Distance

But try the problem first...

Answer:\(\frac{\pi}{10}\)

Source

Suggested Reading

AMC-8, 2014 problem 25

Challenges and Thrills of Pre College Mathematics

First hint

Find the circumference of a semi-circle

Can you now finish the problem ..........

Second Hint

If Robert rides in a straight line, it will take him \(\frac {1}{5}\) hours

can you finish the problem........

Final Step

If Robert rides in a straight line, it will take him \(\frac {1}{5}\) hours. When riding in semicircles, let the radius of the semicircle r, then the circumference of a semicircle is \({\pi r}\). The ratio of the circumference of the semicircle to its diameter is \(\frac {\pi}{2}\). so the time Robert takes is \(\frac{1}{5} \times \frac{\pi}{2}\). which is equal to \(\frac{\pi}{10}\)

- https://www.cheenta.com/area-of-a-square-amc-8-2015-problem-25/
- https://www.youtube.com/watch?v=W9XdZd8zXPA

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