If the angle of a sector is `30^(@)` and the radius of the sector is 21 cm, then length of the arc of the sector is ______.

Options

A. 9 cm
B. 11 cm
C. 10 cm
D. 13 cm

Answer

To find the length of the arc of a sector, we can use the formula:

\[ \text{Length of Arc} = \frac{\theta}{360} \times 2 \pi r \]

where:
- \(\theta\) is the angle of the sector,
- \(r\) is the radius of the sector.

### Step-by-Step Solution:

**Step 1: Identify the given values.**
- Angle of the sector, \(\theta = 30^\circ\)
- Radius of the sector, \(r = 21 \, \text{cm}\)

**Step 2: Substitute the values into the formula.**
\[ \text{Length of Arc} = \frac{30}{360} \times 2 \pi \times 21 \]

**Step 3: Simplify the fraction.**
\[ \frac{30}{360} = \frac{1}{12} \]
So, we can rewrite the equation as:
\[ \text{Length of Arc} = \frac{1}{12} \times 2 \pi \times 21 \]

**Step 4: Calculate \(2 \pi \times 21\).**
Using \(\pi \approx \frac{22}{7}\):
\[ 2 \pi \times 21 = 2 \times \frac{22}{7} \times 21 = \frac{44 \times 21}{7} = \frac{924}{7} = 132 \]

**Step 5: Substitute back into the equation.**
\[ \text{Length of Arc} = \frac{1}{12} \times 132 \]

**Step 6: Calculate the final length of the arc.**
\[ \text{Length of Arc} = \frac{132}{12} = 11 \, \text{cm} \]

### Final Answer:
The length of the arc of the sector is **11 cm**.

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