Answer: r = 4cm/θ
Step-by-step explanation:
For a circle of radius R, the perimeter is:
P = 2*pi*R
Now, if we have an arc with an angle θ, the cord of this arc is:
C = (θ/2*pi)*2*pi*R
Where you can see that if θ = 2*pi (this is the full circle) we have the perimeter of the circle.
In this case, we can see that the cord for an angle θ is 4cm, then:
C = 4cm = (θ/2*pi)*2*pi*r = θ*r
Now we can solve this for r:
r = 4cm/θ
