Question

Points A and B lie on a circle with radius 1, and arc ⌢AB has a length of π/3. What fraction of the circumference of the circle is the length of arc ⌢AB?

Answer 1

⅙

Step-by-step explanation:

Arc as a fraction of the circumference is equal the the central angle as a fraction of total angle in a circle (i.e 2π)

π/3/2π

1/6

Answer 2

1/6

Step-by-step explanation:

The circumference of a circle is denoted by: C = 2πr, where r is the radius. Here, we see that the radius is 1, so plug this in:

C = 2πr

C = 2π * 1 = 2π

We see that arc AB has length π/3, so to find the fraction of the circumference this is, divide π/3 by 2π:

(π/3) ÷ 2π = (π/3) * (1/2π) = 1/6

Thus, the answer is 1/6.