Question

-Shannon's scooter has a piece of tape stuck to the tire. If the tire has a diameter of 18 inches, how far does the piece of tape travel in 72° of rotation?

2π

9π

2 pi over 5

18 pi over 5

Answer 1

`(18\pi)/(5)\ in`

Explanation:

we know that

The formula to calculate the length of an arc of the circle is equal to

`L=(\theta)/(360\°)\pi D`

where

D is the diameter of the circle

`\theta` is the central angle

In this problem we have

`D=18\ in, \theta=72\°`

substitute the values

`L=(72\°)/(360\°)\pi (18)`

`L=(1)/(5)\pi (18)`

`L=(18\pi)/(5)\ in`

Answer 2

Length of an arc = theta/360 * 2pi * r
Distance traveled by the tape = 72/360 * 2pi * 18/2 = 18pi / 5