Question

A bicycle wheel travels 30π inches for each revolution. What is the diameter of the wheel?

Answer 1

The distance traveled is given by:

$S = R \alpha$

Where,

R: bicycle wheel radio

α: central angle

The angle for a revolution is:

$1rev = 2 \pi rad$

Therefore, substituting values we have:

$30\pi = R (2\pi)$

Clearing the radio we have:

$R = \frac{30\pi}{2\pi}$

$R = 15$

Then, the diameter is given by:

$d = 2R$

$d = 2 (15)$

$d = 30$

Answer:

the diameter of the wheel is:

$d = 30in$