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?
Geometry
Semicircle
Distance
Answer:\(\frac{\pi}{10}\)
AMC-8, 2014 problem 25
Challenges and Thrills of Pre College Mathematics
Find the circumference of a semi-circle
Can you now finish the problem ..........
If Robert rides in a straight line, it will take him \(\frac {1}{5}\) hours
can you finish the problem........
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 \(\frac{\pi}{10}\)
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