In a circle of radius 21 cm, an arc subtends an angle of 72 at the centre. The length of the arc is

Options

A. 21.6 cm
B. 26.4 cm
C. 13.2 cm
D. 19.8 cm

Answer

To find the length of the arc in a circle with a radius of 21 cm that subtends an angle of 72 degrees at the center, we can use the formula for the length of an arc:

### Step-by-Step Solution:

1. **Identify the given values**:
- Radius (r) = 21 cm
- Angle subtended at the center (θ) = 72 degrees

2. **Recall the formula for the length of an arc**:
\[ \text{Length of Arc} = \frac{\theta}{360} \times \text{Circumference of the Circle} \]
where the circumference of the circle is given by:
\[ \text{Circumference} = 2\pi r \]

3. **Calculate the circumference of the circle**:
\[ \text{Circumference} = 2 \times \pi \times 21 \]
Using \(\pi \approx \frac{22}{7}\):
\[ \text{Circumference} = 2 \times \frac{22}{7} \times 21 \]
Simplifying:
\[ = \frac{44}{7} \times 21 = \frac{924}{7} = 132 \text{ cm} \]

4. **Substitute the values into the arc length formula**:
\[ \text{Length of Arc} = \frac{72}{360} \times 132 \]

5. **Simplify the fraction**:
\[ \frac{72}{360} = \frac{1}{5} \]

6. **Calculate the length of the arc**:
\[ \text{Length of Arc} = \frac{1}{5} \times 132 = 26.4 \text{ cm} \]

### Final Answer:
The length of the arc is **26.4 cm**.