If the angle of a sector is `45^(@)` and the radius of the sector is 28 cm then the length of the arc is _________.

Answer

To find the length of the arc of a sector, we can use the formula:

\[ \text{Length of Arc} = \frac{\theta}{360} \times 2\pi r \]

where:
- \(\theta\) is the angle of the sector in degrees,
- \(r\) is the radius of the sector.

### Step 1: Identify the values
Given:
- \(\theta = 45^\circ\)
- \(r = 28 \, \text{cm}\)

### Step 2: Substitute the values into the formula
Now, we can substitute the values into the formula for the length of the arc:

\[ \text{Length of Arc} = \frac{45}{360} \times 2\pi \times 28 \]

### Step 3: Simplify the fraction
First, simplify \(\frac{45}{360}\):

\[ \frac{45}{360} = \frac{1}{8} \]

### Step 4: Calculate the length of the arc
Now substitute this back into the equation:

\[ \text{Length of Arc} = \frac{1}{8} \times 2\pi \times 28 \]

Calculating \(2\pi \times 28\):

\[ 2\pi \times 28 = 56\pi \]

Now substitute this into the equation:

\[ \text{Length of Arc} = \frac{1}{8} \times 56\pi \]

### Step 5: Final calculation
Now calculate \(\frac{56\pi}{8}\):

\[ \frac{56\pi}{8} = 7\pi \]

### Step 6: Approximate the value (if necessary)
If we need a numerical approximation, we can use \(\pi \approx 3.14\):

\[ 7\pi \approx 7 \times 3.14 = 21.98 \, \text{cm} \]

Thus, the length of the arc is:

\[ \text{Length of Arc} \approx 21.98 \, \text{cm} \]

### Final Answer:
The length of the arc is \(7\pi \, \text{cm}\) or approximately \(21.98 \, \text{cm}\).

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