Question

The formula for the circumference of a circle is , where C = circumference and d =
diameter. It can also be defined as , where r = radius. If 360 degrees = radians, and the
formula for arc length is the determine the length created by a 30 degree central angle in a
circle with a 2 inch diameter and explain how you found it. Leave your answer in terms of pi. You may
type out your work or upload it. (3 points)
C = πd
C = 2πr 2π
θ = , s
r
0

Answer 1

Diameter = 2 in, so radius r = 1 in.

Method 1 (fraction of circumference):
- Circumference C = 2πr = 2π(1) = 2π.
- A 30° central angle is 30/360 = 1/12 of the circle.
- Arc length s = (1/12)·C = (1/12)·2π = π/6 in.

Method 2 (radians and s = rθ):
- 30° = 30·(π/180) = π/6 radians.
- s = r·θ = 1·(π/6) = π/6 in.

Answer: π/6 inches.