Geometry Homework

Question

The radius of a circle is 3 meters. What is the length of a 180 degree arc? In simplest form.

Answer 1

The 180⁰ arc should tell you we're looking at 1/2 the circumference of the circle.

If S = rθ and 180⁰ = π = θ then S (which is the element of arc length) = (3m) π or 3π m.

Answer 2

Method 1:

The arc length, s, is:

s = rθ

Then, the subtended angle is θ = 180° = π radians

s = rθ = (3m)(π radians) = 3π m

Method 2:

The shape is a semicircle with an angle of 180° = π radians.

The arc length of a semicircle is half the circumference of a full circle of the same radius:

s = (1/2)(2πr) = πr = π(3 m) = 3π m