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

## Circumference of a Semicircle- AMC 8, 2014 – Problem 25

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?

• $\frac{\pi}{11}$
• $\frac{\pi}{10}$
• $\frac{\pi}{5}$

### Key Concepts

Geometry

Semicircle

Distance

But try the problem first…

Answer:$\frac{\pi}{10}$

Source

AMC-8, 2014 problem 25

Challenges and Thrills of Pre College Mathematics

## Try with Hints

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 $\frac{\pi}{10}$