Question

In circle L, arc OP is 45 degrees and the radius is 5 units. Which statement best describes the length of arc OP ?

Answer 1

1/8 the circumference of circle L

Explanation:

I just took the test and got it right

Answer 2

The length of arc OP is 1/8 the circumference of the circle

Explanation:

step 1

Find the circumference of the circle L

The circumference is equal to

`C=2\pi r`

we have

`r=5\ units`

substitute

`C=2\pi (5)`

`C=10\pi\ units`

step 2

Find the length of arc OP

we know that the circumference of the circle subtends a central angle of 360 degrees

so

using proportion

Find out the length of the arc OP by a central angle of 45 degrees

Let

x -----> the length of arc OP

`(10\pi)/(360)=(x)/(45)\\\\x=10\pi(45)/360\\\\x=10\pi((1)/(8))\ units`

therefore

The length of arc OP is 1/8 the circumference of the circle