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
Accepted Solution
A:
Answer:[tex]9\pi\ ft[/tex]Step-by-step explanation:step 1Find the circumference of the circleThe circumference is equal to[tex]C=2\pi r[/tex]we have[tex]r=6\ ft[/tex]substitute[tex]C=2\pi(6)[/tex][tex]C=12\pi\ ft[/tex]step 2we know thatThe circumference of a circle subtends a central angle of 2π radianssousing proportionFind out the length of the arc for a central angle of 3π/2 radiansLet x------> the length of the arc[tex]\frac{12\pi}{2\pi}=\frac{x}{3\pi/2} \\ \\x=9\pi\ ft[/tex]