The value of the central angle φ for Circle 2 is 36 radians.
Step-by-step explanation:
For Circle 1: The radius is given as 6 units and the intercepted arc of the central angle is given as 8π units. Since the intercepted arc is equal to the circumference of a circle with radius 6, we can set up the equation:
8π = 2π(6)
Dividing both sides by 2π, we get the central angle for Circle 1 as 6 radians.
For Circle 2: The diameter is given as 36 units and the intercepted arc of the central angle is given as 24π units. Since the intercepted arc is equal to the circumference of a circle with diameter 36, we can set up the equation:
24π = π(36)
Dividing both sides by π, we get the central angle φ for Circle 2 as 36 radians.
The probable question can be: Two circles include central angles. The circles are described below. Circle 1: Radius =6. Central angle =0. Intercepted arc of the central angle =8π. a Circle 2: Diameter =36. Central angle = φ. Intercepted arc of the central angle =24π. Explore the relationships between the given parameters and determine the value of the central angle φ for Circle 2.