Cheenta
How 9 Cheenta students ranked in top 100 in ISI and CMI Entrances?
Learn More

Circumference of a Semicircle | AMC 8, 2014 | Problem 25

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?

circumference of a semicircle

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

Key Concepts


Geometry

Semicircle

Distance

Check the Answer


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

AMC-8, 2014 problem 25

Challenges and Thrills of Pre College Mathematics

Try with Hints


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........

circumference of a semicircle

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

Subscribe to Cheenta at Youtube


Knowledge Partner

Cheenta is a knowledge partner of Aditya Birla Education Academy
Cheenta

Cheenta Academy

Aditya Birla Education Academy

Aditya Birla Education Academy

Cheenta. Passion for Mathematics

Advanced Mathematical Science. Taught by olympians, researchers and true masters of the subject.
JOIN TRIAL
support@cheenta.com