Final answer:
By converting the angle of 72° to radians and applying the arc length formula, the radius of the wheel is calculated as 120 cm. This does not match any of the available options, suggesting a possible error in the given values.
Step-by-step explanation:
To solve for the radius of the wheel when an arc length of 24π cm subtends an angle of 72° at the center, we can use the relationship between arc length (s), radius (r), and central angle (θ) in radians. The formula for arc length is s = rθ, where r is the radius and θ is the angle in radians.
Firstly, we convert the central angle from degrees to radians by using the conversion ratio: 180° = π radians. Hence:
θ = (72° × π) / 180° = π/5 radians.
Now we can plug the values into the arc length formula:
24π = r(π/5)
r = (24π) / (π/5) = 120 cm.
This is not an available option, meaning there might be an error in the provided arc length or options. However, using the provided arc length, the calculated radius does not match any given choices (a. 50 cm, b. 40 cm, c. 30 cm, d. 60 cm).