Answer:
Option 4 - [tex]L=9\pi ft.[/tex]
Step-by-step explanation:
Given : In a circle with a radius of 6 ft, an arc is intercepted by a central angle of 3π/2 radians.
To find : What is the length of the arc?
Solution :
Length of an arc is given by:
[tex]L=r\theta[/tex]
where r is the radius of the circle, r= 6 ft.
and [tex]\theta[/tex] is the angle in radian, [tex]\theta=\frac{3\pi }{2}[/tex]
Substitute the value given in the formula,
[tex]L=r\theta[/tex]
[tex]L=6\times \frac{3\pi }{2}[/tex]
[tex]L=3\times3\pi[/tex]
[tex]L=9\pi[/tex]
Therefore, Option 4 is correct.
The arc of length is [tex]L=9\pi ft.[/tex]
