The area of a sector of angle `theta^(@)` of a circle with radius `R` is

Options

A. `(2piRtheta)/180`
B. `(piR^(2)theta)/180`
C. `(2piRtheta)/360`
D. `(piR^(2)theta)/360`

Explanation

To find the area of a sector of a circle with a given radius \( R \) and angle \( \theta \), we can use the following formula:

### Step-by-Step Solution:

1. **Understand the Formula**: The area \( A \) of a sector of a circle can be calculated using the formula:
\[ A = \frac{\theta}{360} \times \pi R^2 \]
where \( \theta \) is the angle in degrees and \( R \) is the radius of the circle.

2. **Identify the Given Values**: From the problem, we have:
- Radius \( R \)
- Angle \( \theta \) (in degrees)

3. **Substitute the Values**: Plug the values of \( R \) and \( \theta \) into the formula. For example, if \( R = 5 \) units and \( \theta = 60^\circ \):
\[ A = \frac{60}{360} \times \pi \times (5)^2 \]

4. **Simplify the Expression**: Calculate the fraction:
\[ A = \frac{1}{6} \times \pi \times 25 \]
\[ A = \frac{25\pi}{6} \]

5. **Final Result**: The area of the sector is:
\[ A = \frac{25\pi}{6} \text{ square units} \]