In a circle of radius 42 cm, an arc subtends an angle of `72^(@)` at the centre. The length of the arc is?

Options

A. A)52.8 cm
B. B)53.8 cm
C. C)72.8 cm
D. D)79.8 cm

Answer

To find the length of the arc in a circle with a radius of 42 cm that subtends an angle of 72 degrees at the center, we can use the formula for the length of an arc:

**Arc Length (L) = (θ/360) × (2πr)**

Where:
- θ is the angle in degrees,
- r is the radius of the circle.

### Step-by-Step Solution:

1. **Identify the values:**
- Radius (r) = 42 cm
- Angle (θ) = 72 degrees

2. **Substitute the values into the formula:**
\[ L = \left(\frac{72}{360}\right) \times (2 \times \pi \times 42) \]

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

4. **Calculate the circumference of the circle:**
\[ 2 \times \pi \times 42 = 84\pi \text{ cm} \]

5. **Now substitute back into the arc length formula:**
\[ L = \frac{1}{5} \times 84\pi \]

6. **Calculate the arc length:**
\[ L = \frac{84\pi}{5} \]

7. **Using the approximate value of π (22/7):**
\[ L = \frac{84 \times \frac{22}{7}}{5} \]

8. **Simplifying further:**
\[ L = \frac{1848}{35} \]

9. **Calculating the final value:**
\[ L = 52.8 \text{ cm} \]

### Final Answer:
The length of the arc is **52.8 cm**.

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