Question

An arc is intercepted by a central angle of 3π2 radians on a circle with a radius of 18 centimeters. What is the exact length of the arc? Enter your answer, in terms of π , in the box.

Answer 1

The length of the arc is
`27\pi \ cm`

Explanation:

step 1

Find the circumference

we know that

The length of a complete circle is equal to the circumference of the circle

The circumference is equal to

`C=2\pi r`

we have

`r=18\ cm`

substitute

`C=2\pi (18)`

`C=36\pi\ cm`

step 2

we know that

A central angle of
`2\pi` radians subtends the circumference of
`36\pi\ cm`

so

by proportion

Find the length of the arc by a central angle of
`(3\pi )/(2)` radians

`(36\pi )/(2\pi)(cm)/(radians)=(x)/((3\pi/2))(cm)/(radians) \\ \\x=18*(3\pi/2)\\ \\x=27\pi \ cm`