Question

Find the length of AB

Answer 1

AB = 3π

Explanation:

The formula for the circumference of a circle is:

C = 2πr

By substituting 27 for r:

C = 2π(27)

C = 54π

The whole circumference is 54π. A circle is 360º around. We can set up a proportion to find the length of the 20º arc:

`(360)/(54p)` =
`(20)/(x)`

Cross-multiply:

360x = 1080π

Divide both sides by 360:

x = 3π

AB = 3π

Answer 2

AB = 3π

Explanation:

The arc AB can be calculated as

AB = circumference of circle × fraction of circle

The central angle is equal to the measure of arc AB = 20° , thus

AB = 2πr ×
`(20)/(360)`

= 2π × 27 ×
`(1)/(18)` ( cancel 18 and 27 by 9 )

= 2π × 3 ×
`(1)/(2)` = 6π ×
`(1)/(2)` = 3π