In a circle of radius 21 cm, an arc subtends an angle of 60° at the centre. Find :
Area of the sector formed by the arc

Answer

To find the area of the sector formed by the arc in a circle of radius 21 cm that subtends an angle of 60° at the center, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the given values:**
- Radius of the circle (r) = 21 cm
- Angle subtended at the center (θ) = 60°

2. **Use the formula for the area of a sector:**
The formula for the area of a sector is given by:
\[ \text{Area of sector} = \frac{\pi r^2 \theta}{360} \]
where:
- \( r \) = radius of the circle
- \( \theta \) = angle in degrees

3. **Substitute the values into the formula:**
\[ \text{Area of sector} = \frac{\pi \times (21)^2 \times 60}{360} \]

4. **Calculate \( r^2 \):**
\[ (21)^2 = 441 \]

5. **Substitute \( r^2 \) back into the formula:**
\[ \text{Area of sector} = \frac{\pi \times 441 \times 60}{360} \]

6. **Simplify the fraction:**
- First, simplify \( \frac{60}{360} = \frac{1}{6} \).
- Now, the formula becomes:
\[ \text{Area of sector} = \frac{\pi \times 441}{6} \]

7. **Calculate \( \frac{441}{6} \):**
\[ \frac{441}{6} = 73.5 \]

8. **Now multiply by \( \pi \) (using \( \pi \approx \frac{22}{7} \)):**
\[ \text{Area of sector} = 73.5 \times \frac{22}{7} \]

9. **Calculate \( 73.5 \times \frac{22}{7} \):**
- First, calculate \( 73.5 \times 22 = 1617 \).
- Then divide by 7:
\[ \frac{1617}{7} = 231 \]

10. **Final answer:**
\[ \text{Area of the sector} = 231 \text{ cm}^2 \]