Question

The formula for the circumference of a circle is C=πd
, where C=
circumference and d=
diameter. It can also be defined as C=2πr
, where r=
radius. If 360 degrees =2π
radians, and the formula for arc length is θ=sr
, then determine the length created by a 60-degree central angle in a circle with a 2-inch diameter and explain how you found it. Answer in 3–5 sentences.(4 points)

Answer 1

The diameter is 2 in so the radius r = 1 in. A 60° angle equals 60°·(π/180°) = π/3 radians, and arc length s = rθ = 1·(π/3) = π/3 inches. Numerically this is about 1.047 inches. (Equivalently, 60° is 1/6 of the circle, and 1/6 of the circumference 2π(1) = 2π gives 2π/6 = π/3.)