Find length of the arc whose central angle is `45^@` and radius of the circle is 28 cm.

Options

A. 11 cm.
B. 33 cm.
C. 44 cm.
D. 22 cm.

Answer

To find the length of the arc of a circle given the central angle and the radius, we can use the formula for the length of an arc (L):

\[ L = \frac{\theta}{360} \times 2\pi r \]

where:
- \(L\) is the length of the arc,
- \(\theta\) is the central angle in degrees,
- \(r\) is the radius of the circle.

### Step-by-Step Solution:

1. **Identify the given values:**
- Central angle, \(\theta = 45^\circ\)
- Radius, \(r = 28 \, \text{cm}\)

2. **Substitute the values into the arc length formula:**
\[ L = \frac{45}{360} \times 2\pi \times 28 \]

3. **Simplify the fraction:**
\[ \frac{45}{360} = \frac{1}{8} \]
So, we can rewrite the equation as:
\[ L = \frac{1}{8} \times 2\pi \times 28 \]

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

5. **Substitute \(2\pi\) back into the equation:**
\[ L = \frac{1}{8} \times \frac{44}{7} \times 28 \]

6. **Calculate \(28 \div 8\):**
\[ 28 \div 8 = 3.5 \]
Thus, we can rewrite the equation:
\[ L = \frac{44}{7} \times 3.5 \]

7. **Calculate \(44 \times 3.5\):**
\[ 44 \times 3.5 = 154 \]

8. **Divide by 7:**
\[ L = \frac{154}{7} = 22 \, \text{cm} \]

### Final Answer:
The length of the arc is \(22 \, \text{cm}\).

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