In a circle of radius 21 cm, an arc subtends an angle of `60^(@)` at the centre. The length of the arc is

Options

A. 21 cm
B. 22 cm
C. 18.16 cm
D. 23.5cm

Explanation

To find the length of the arc in a circle with a radius of 21 cm and an angle of 60 degrees at the center, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the given values:**
- Radius (r) = 21 cm
- Angle (θ) = 60 degrees

2. **Use the formula for the length of an arc:**
The formula for the length of an arc (l) is given by:
\[ l = \frac{\theta}{360} \times 2\pi r \]
where θ is in degrees.

3. **Substitute the values into the formula:**
\[ l = \frac{60}{360} \times 2\pi \times 21 \]

4. **Simplify the fraction:**
\[ \frac{60}{360} = \frac{1}{6} \]
Now substitute this back into the equation:
\[ l = \frac{1}{6} \times 2\pi \times 21 \]

5. **Calculate the multiplication:**
\[ l = \frac{1}{6} \times 42\pi \]
\[ l = 7\pi \]

6. **Use the approximate value of π (if needed):**
If we take π as \(\frac{22}{7}\):
\[ l = 7 \times \frac{22}{7} = 22 \text{ cm} \]

### Final Answer:
The length of the arc is **22 cm**.

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