Question

In a circle with a radius of 6 ft, an arc is intercepted by a central angle of 3π2 radians.

What is the length of the arc?


2π ft

​ 3π ​ ft

​ 6π ​ ft

​ 9π ​ ft

Answer 1

​ 9π ​ ft

Explanation:

took the test to prove the answer right. picture below

Answer 2

`9\pi\ ft`

Explanation:

step 1

Find the circumference of the circle

The circumference is equal to

`C=2\pi r`

we have

`r=6\ ft`

substitute

`C=2\pi(6)`

`C=12\pi\ ft`

step 2

we know that

The circumference of a circle subtends a central angle of 2π radians

so

using proportion

Find out the length of the arc for a central angle of 3π/2 radians

Let

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

`(12\pi)/(2\pi)=(x)/(3\pi/2) \\ \\x=9\pi\ ft`