Answer:
Option 4 - \(L=9\pi ft.\)
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:
\(L=r\theta\)
where r is the radius of the circle, r= 6 ft.
and \(\theta\) is the angle in radian, \(\theta=\frac{3\pi }{2}\)
Substitute the value given in the formula,
\(L=r\theta\)
\(L=6\times \frac{3\pi }{2}\)
\(L=3\times3\pi\)
\(L=9\pi\)
Therefore, Option 4 is correct.
The arc of length is \(L=9\pi ft.\)
