Question

The arc length of the shaded part of the circle is 2pi inches.

Which equation can be used to find the circumference of the entire circle, C?

Answer 1

2pi/C = 45/360

Explanation:

L = arc length

C = circumference

x = central angle

Tying those three variables together leads us to this

L = (x/360)*C

The idea is we effectively take a fraction of the circumference to end up with the arc length.

In the formula above, we can rearrange terms to get

L = (x/360)*C

360L = Cx

L/C = x/360

We know that L = 2pi and x = 45, which means we end up with

L/C = x/360

2pi/C = 45/360