Question

1. gears on a bicycle are just circles in shape. one gear has a diameter of 4\, and a smaller one has a diameter of 2\. how much bigger is the circumference of the larger one compared to the smaller one?

Explanation:

Step1: Recall circumference formula

The circumference of a circle is $C = \pi d$, where $d$ is diameter.

Step2: Calculate larger gear circumference

For $d=4''$, $C_{large} = \pi \times 4 = 4\pi$

Step3: Calculate smaller gear circumference

For $d=2''$, $C_{small} = \pi \times 2 = 2\pi$

Step4: Find ratio of circumferences

$\frac{C_{large}}{C_{small}} = \frac{4\pi}{2\pi} = 2$

Answer:

The circumference of the larger gear is 2 times bigger than the smaller one, or $4\pi - 2\pi = 2\pi$ inches longer.