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

To solve this question, we need to find the length of the arc of a sector in a circle. The formula for the length of the arc of a sector is given by:

\(L = \frac{\theta}{360^{\circ}} \times 2\pi r\)

where:

• \(\theta\) is the central angle in degrees,
• \(r\) is the radius of the circle,
• \(L\) is the length of the arc,
• \(\pi \approx 3.1416\).

Given:

• Radius \((r) = 21 \, \text{cm}\)
• Central angle \((\theta) = 60^{\circ}\)

Substitute these values into the formula:

\(L = \frac{60}{360} \times 2 \times 3.1416 \times 21\)

Simplify the calculation:

1. \(\frac{60}{360} = \frac{1}{6}\)
2. \(L = \frac{1}{6} \times 2 \times 3.1416 \times 21 = \frac{1}{3} \times 3.1416 \times 21\)
3. Approximate the multiplication:
   \(= \frac{1}{3} \times 66 = 22\) (since \(3.1416 \approx \frac{22}{7}\) and \(\frac{22}{7} \times 21 \approx 66\))

Therefore, the length of the arc is 22 cm.