The area of a sector of a circle of radius 8 cm , formed by an arc of length 5.6 cm , is :

Options

A. `22 cm^(2) `
B. `2.24 cm^(2) `
C. `56 cm^(2) `
D. none of these

Answer

To find the area of a sector of a circle when the radius and the length of the arc are given, we can use the formula:

\[ \text{Area of Sector} = \frac{1}{2} \times \text{Length of Arc} \times \text{Radius} \]

Given:
- Radius (r) = 8 cm
- Length of Arc (L) = 5.6 cm

### Step 1: Substitute the values into the formula
We will substitute the values of the length of the arc and the radius into the formula for the area of the sector.

\[ \text{Area of Sector} = \frac{1}{2} \times 5.6 \times 8 \]

### Step 2: Calculate \(\frac{1}{2} \times 8\)
First, we calculate \(\frac{1}{2} \times 8\):

\[ \frac{1}{2} \times 8 = 4 \]

### Step 3: Multiply by the length of the arc
Now, we multiply this result by the length of the arc (5.6 cm):

\[ \text{Area of Sector} = 4 \times 5.6 \]

### Step 4: Perform the multiplication
Now we calculate \(4 \times 5.6\):

\[ 4 \times 5.6 = 22.4 \, \text{cm}^2 \]

### Final Answer
The area of the sector is:

\[ \text{Area of Sector} = 22.4 \, \text{cm}^2 \]