Given that an intercepted arc has length 6π inches and the central angle is pie/3 , find the radius of the circle.
To find the radius of the circle, we can use the formula relating the length of an intercepted arc, the central angle, and the radius of the circle:
Length of intercepted arc = r * θ
Where:
r = radius of the circle
θ = central angle in radians
Given that the length of the intercepted arc is 6π inches and the central angle is π/3, we can plug in the values into the formula:
6π = r * π/3
To solve for r, we can divide both sides by π/3:
r = 6π / (π/3)
r = 6π * 3/π
r = 18 inches
Therefore, the radius of the circle is 18 inches.