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?

Question

anonymous · Answer

dont you find the radians of the degree first?

anonymous · Answer

This is a pretty interesting and a fun yet simple question! it's just all about how well you imagine this in your head :)

anonymous · Answer

Okay so lets draw ourselves a circle first, shall we?

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our $$d = 18 $$

anonymous · Answer

if our d = 18 then our r = 9  right?

okay you should start imagining the arc in this, if our degree is 72° (which is a positive degree, we can consider this positive degree moving counterclockwise) like this:

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anonymous · Answer

now you can convert the degree to radians if you wish, to convert 72° to degree to radians 
then you should probably be familiar with the pi and 180° ratio

$$\pi rad = 180°$$
$$\frac{ \pi }{ 180 }rad  = 1°$$

anonymous · Answer

so if 1° gives $$\frac{ \pi }{ 180 }rad$$ 

then 72° should give $$\frac{ 2 }{ 5 }\pi rad$$

anonymous · Answer

the formula to find the arc length in a radian is
$$S = \theta*r$$

anonymous · Answer

we have our radius and we have our theta so all you need to do is plug the numbers into the formula

$$S = \frac{ 2\pi }{ 5 } * 9$$
$$S = \frac{ 18 }{ 5 }\pi$$

so the tape moved 11.309 inches