Arc length from radius and angle: In a circle of radius 21 cm, an arc subtends a central angle of 72°. Find the length of this arc.

Introduction / Context:Arc length is the same fraction of the full circumference as the angle is of 360°. With radius and angle known, the computation is straightforward.

Given Data / Assumptions:

• r = 21 cm
• θ = 72°
• Full circumference = 2πr

Concept / Approach:L = (θ/360) * 2πr. Substitute values and simplify.

Step-by-Step Solution:L = (72/360) * 2π * 21 = (1/5) * 42π = 8.4π cmWith π = 22/7, L = 8.4 * 22/7 = 26.4 cm

Verification / Alternative check:Using π ≈ 3.1416 gives L ≈ 26.39 cm, which rounds to 26.4 cm, matching the option.

Why Other Options Are Wrong:Other lengths correspond to different angles or radii; they do not match the 72° fraction of the full circumference.

Common Pitfalls:Using degree measure incorrectly (forgetting the /360 factor); using diameter instead of radius.

Final Answer:26.4 cm