Arc length with central angle 30° and radius 21 cm\nFind the length of the arc (in cm) subtended by a central angle of 30° in a circle of radius 21 cm.

Introduction / Context:
Arc length for central angle θ (in degrees) uses s = (θ/360) * 2πr. Substituting θ = 30° simplifies to one-twelfth of the circumference, which is convenient for mental checks too.

Given Data / Assumptions:

• θ = 30°, r = 21 cm
• Use π = 22/7 (or 3.14) for evaluation.

Concept / Approach:
Compute s = (30/360) * 2πr = (1/12) * 2πr = (1/6) * πr. With r = 21, this becomes (1/6)*π*21 = 3.5π, which is close to 11 when π ≈ 22/7.

Step-by-Step Solution:

Verification / Alternative check:
Using π ≈ 3.14 ⇒ 3.5 * 3.14 ≈ 10.99 cm, which rounds to 11 cm, matching the choice.

Why Other Options Are Wrong:
16.5 and 22 assume larger angles; 28 is a radius multiple not tied to 30°. Only 11 cm fits exactly.

Common Pitfalls:
Mixing degrees with radians or forgetting to divide by 360 when θ is in degrees is common.

Final Answer:
11 cm