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

Answer:

To figure out the answer to this question, you'll first need to know the formula for finding the circumference of a circle.

The circumference, C, of a circle is C=2πr, where r is the radius of the circle. For the given circle with a radius of 1, the circumference is C=2(π)(1), or C=2π.

To find what fraction of the circumference the length of

⌢

AB

is, divide the length of the arc by the circumference, which gives

π

3

÷2π. This division can be represented by

π

3

*

1

2

π=

1

6

.

The fraction

1

6

can also be rewritten as 0.166 or 0.167.

The final answer is

1

6

, 0.166, or 0.167.