Final answer:
The arc length of a circle with a 21-inch radius and a central angle of 4π/7 radians is 84/7π inches, option a.
Step-by-step explanation:
The question asks to calculate the length of an arc in a circle with a radius of 21 inches, intercepted by a central angle of 4π/7 radians. To find the arc length, we use the formula:
arc length (s) = radius (r) × central angle (θ)
Since the radius of the circle (r) is 21 inches and the central angle (θ) is 4π/7 radians, we can plug these values into the formula to find the arc length:
s = 21 inches × (4π/7)
By multiplying these values, we get:
s = (21 × 4π/7) inches
Simplifying the expression:
s = (84π/7) inches
Therefore, the correct answer is 84/7π inches, which corresponds to option a.