The area of a sector of a circle of radius 5 cm, formed by an arc of length 3.5 cm is

Options

A. (a) `8.5 cm^(2)`
B. (b) `8.75 cm^(2)`
C. (c) `7.75 cm^(2)`
D. (d) `7.50 cm^(2)`

Answer

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

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

### Step-by-Step Solution:

1. **Identify the given values:**
- Radius (r) = 5 cm
- Arc Length (L) = 3.5 cm

2. **Substitute the values into the formula:**
\[ \text{Area of the sector} = \frac{1}{2} \times 3.5 \, \text{cm} \times 5 \, \text{cm} \]

3. **Calculate the area:**
- First, calculate the product of the arc length and the radius:
\[ 3.5 \, \text{cm} \times 5 \, \text{cm} = 17.5 \, \text{cm}^2 \]
- Now, multiply by \(\frac{1}{2}\):
\[ \text{Area of the sector} = \frac{1}{2} \times 17.5 \, \text{cm}^2 = 8.75 \, \text{cm}^2 \]

4. **Final Result:**
The area of the sector is \(8.75 \, \text{cm}^2\).

### Conclusion:
The correct answer is \(8.75 \, \text{cm}^2\).

---