Question

A bicycle wheel is 63m in diameter. how many metres does the bicycle travel for 100 revolutions of the wheel. (pie=²²/⁷)​

Answer 1

let's reword it

what is the arc of a circle whose central angle is 100 revolutions and has a radius of 63÷2?

let's keep in mind that radius is half the diameter, and a revolution is 2π radians or 360°, so hmmm 100 revolutions will just be 360*100 = 36000°.

`\textit{arc's length}\\\\ s = \cfrac{\theta \pi r}{180} ~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ \theta =36000\\ r=(63)/(2) \end{cases}\implies s=\cfrac{(36000)\pi ((63)/(2))}{180}\implies s=\cfrac{(36000)((22)/(7)) ((63)/(2))}{180} \\\\\\ s=200((22)/(7)) ((63)/(2))\implies s=(200)(99)\implies \boxed{s=19800}~metres`

Answer 2

Answer: 1979.2 meters

Explanation:

Diameter of wheel is 63 cm. Circumference is 63π = 197.92 cm. 1000 revolutions of 197.92 = 197920 cm = 1979.2 meters.