Question

The length of the arc of the sector of a circle with radius 21 cm and of central angle 60°, is :

• A. 22 cm
• B. 44 cm
• C. 88 cm
• D. 11 cm

Hint:

Since \( 60^\circ \) is exactly \( 1/6 \) of a circle, the arc length is simply the circumference divided by 6.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
The length of an arc is a fraction of the total circumference of the circle, determined by the ratio of the central angle to \( 360^\circ \).
Step 2: Key Formula or Approach:
\[ \text{Arc Length} = \frac{\theta}{360^\circ} \times 2\pi r \]
Step 3: Detailed Explanation:
1. Given radius \( r = 21 \) cm and \( \theta = 60^\circ \). 2. Substitute into the formula: \[ \text{Arc Length} = \frac{60}{360} \times 2 \times \frac{22}{7} \times 21 \] 3. Simplify the terms: \[ \text{Arc Length} = \frac{1}{6} \times 2 \times 22 \times 3 \] \[ \text{Arc Length} = \frac{1}{6} \times 132 \] \[ \text{Arc Length} = 22 \text{ cm} \]
Step 4: Final Answer:
The length of the arc is 22 cm.