Question

A 100 degree arc of a circle has a length of 7cm. To the nearest centimeter, what's the radius of the circle?
Please help emergency! Medal/fan

Answer 1

The arc length of a circle is defined as follows:

$$ s = \theta r $$


You have s and theta, now just algebraically solve for r

Answer 2

But what's s in this problem

Answer 3

s is the arc length :)

Answer 4

Oh thanks!!! Are u up for one more?

Answer 5

Sure!

Answer 6

Mr. H races on a bike with 26 inch diameter wheels. When he is traveling at a speed of 44 ft/sec, how many revolutions per min are his wheels making?

Answer 7

Okay, let's first get everything in similar units. It will be easier to work in inches, since it will give us whole numbers.

44 ft = how many inches?

Answer 8

528 inches

Answer 9

Bueno. So every second, Mr. H is traveling 528 inches.

This is where arc length is useful!

Answer 10

The arc length is just like saying, if you laid the rubber of the tire out as a line, how long would it be?

Answer 11

How does that apply here?

Answer 12

Well, we need to find the arc length of the tire in order to find out how many rotations per second he is making

Answer 13

So, we know that

$$ s = \theta r $$

We need the radius. Do you know how to get the radius from the diameter?

Answer 14

ya
26/2 = 13

Answer 15

Perfect, so the diameter is 13 in.

Now, how many degrees are in a full circle?

Answer 16

360

Answer 17

Great. So the arc length is?

Answer 18

whats theta in this case