for a circle with arc length 8(pi)/3 ft and a central angle of 60 degrees, find the radius.

Question

This problem involves finding the radius of a circle. 

Answer 1

Hi Ava,

 

Arc length formula is:  Arc Length = (pi * radius * central angle)/180

 

So if you know the Arc Length and the central angle, plug all of that in and solve for the radius.

 

 

In for Arc Length will go 8pi/3

In for central angle will go 60

 

 

 

8*pi/3 = (pi * radius * 60) / 180

 

Simplify the right side:

 

8pi/3 =   (pi * radius)/3

 

Divide both sides by pi.

 

8/3 = radius/3

 

Multiply both sides by 3

 

8 = radius

 

 

Final answer:  radius = 8