Question

vincent was riding a bicycle with wheels 24 inches in diameter. during 5 minutes of his ride, his wheels made exactly 1,000 revolutions. which of the following provides the best estimate for the distance vincent traveled, in feet, for those 5 minutes? 1,250π 2,000π 3,250π 5,000π

Explanation:

Step1: Calculate the circumference of the wheel

The formula for the circumference of a circle is \(C = \pi d\). Given \(d = 24\) inches, so \(C=24\pi\) inches.

Step2: Convert inches to feet

Since \(1\) foot \( = 12\) inches, then \(C=\frac{24\pi}{12}=2\pi\) feet.

Step3: Calculate the total distance

The wheel made \(n = 1000\) revolutions. The total distance \(D=n\times C\). Substitute \(n = 1000\) and \(C = 2\pi\) into the formula, we get \(D=1000\times2\pi=2000\pi\) feet.

Answer:

\(2000\pi\)