Question

Find the length of AC express your answer in terms of pie

Answer 1

The length of arc AC is
`15\pi\ cm`

Explanation:

step 1

Find the circumference of the circle

The circumference is equal to

`C=\pi D`

we have

`D=36\ cm`

substitute

`C=\pi (36)`

`C=36\pi\ cm`

step 2

Find the length of arc AC

Remember that the circumference subtends a central angle of 360 degrees

The measure of arc AC is equal to

arc AC+30°=180° ----> because the diameter divide the circle into two equal parts

arc AC=180°-30°=150°

using proportion

`(36\pi)/(360)=(x)/(150)\\ \\x=36\pi*150/360\\ \\x=15\pi\ cm`