Question

What is the length of the indicated arc? (7/2 pi) (14 pi) (3.5 pi) (7 pi), or (none of the above)

Answer 1

Know the formula for arc length?

Answer 2

If you think about it, the circumference of a circle is the measure of the arc length for a full 360 degrees. So \(2\pi r\) is the arc length for 360. You can then use that and a ratio to find what it is for 315.

Answer 3

I got 25.12

Answer 4

Well, you don't want to used 3.14 for pi. All the answers are exact. And let me see if that is right.

Answer 5

ok

Answer 6

Hmmm... That is not what I got.

OK, do you know what the ratio or fraction you need to multiply by would be?

Answer 7

If you know how to convert from degrees to radians, that is another way to set it up. Ends up being the same thing in the end.

Answer 8

No I'm trying to figure it out but idk

Answer 9

OK. For any ratio like this, you are looking for a percentage of the whole. In general, that is the fraction:

\(\dfrac{\rm portion}{\rm whole}\)

Answer 10

In this specific case, your potion is the degrees of the arc and the whole is the degrees of a circle.

Answer 11

so something divided by 360 degrees

Answer 12

Exactly! The degrees of the arc divided by 360.

Answer 13

315 divided by 360?

Answer 14

Yes. And you multiply that by the circumference, or \(2\pi r\). Now, because the answer has \(\pi\) in it, you can leave it out of the multiplying. So don't multiply by 3.14 because you know the "(7/2 pi) (14 pi) (3.5 pi) (7 pi) or none" takes that into account.

Answer 15

ok 315 divided by 360 is 0.875, then what if I can't multiply 3.14

Answer 16

Well, 2pi r without the pi is 2r. So multiply by 2r.

Answer 17

8

Answer 18

So 8 * .875

Answer 19

I get 70

Answer 20

70? Umm.... must have did something wrong.

Answer 21

7, I mean

Answer 22

=) And the pi is still there, we just did not multiply it, so \(7\pi\).

Answer 23

Thank you so much, This one problem helped with like four of my others and I made a 100 thank you, you're genius, I will now grant you your medal!

Answer 24

Glad you were able to learn how it worked. =)

Answer 25

Thanks Costello, anyways I got 3.75 for this ... IDK if it's right

Answer 26

3.75 for what?

Answer 27

oops... I accidentally wrote on the wrong question thread ...

Answer 28

But actually, you are the only person who I can understand this math from , so can you help me with one more problem

Answer 29

It's the latest one that I've put in the posts.