Question

Given that an intercepted arc has length 6π inches and the central angle is pie/3 , find the radius of the circle.

Answer 1

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.