Question

What is the length of the arc with a measure of 200 degrees in a circle with a radius of 31 inches?

Answer 1

403π/9 or 140.67

Explanation:

First, you have to find the circumference of the circle

Circle circumference equation:

Circumference = dπ (Circumference = diameter x pi)

You have a radius of 31 which is equal to 62 diameter (diameter is double the radius)

So:

C = 62π

Now, you need to know that a full circle is 360 degrees and we want only 200 degrees of that,

So in other words, you want 200/360 of the circle's circumference.

You can find the measure of the 200 degree arc by doing

62π x
`(200)/(360)` =
`(403pi)/(9)` or 140.67