Area of a sector of angle p (in degrees) of a circle with radius R is

Options

A. `(p)/( 180) xx 2piR`
B. `(p) /(180) xx pi R^2`
C. `(p)/(360) xx 2pi R`
D. `(p)/( 360) xx pi R^2`

Answer

To find the area of a sector of a circle with a given angle \( P \) (in degrees) and radius \( R \), we can follow these steps:

### Step-by-Step Solution:

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

2. **Identify the Given Values**: In this case, we have:
- Angle \( P \) (in degrees)
- Radius \( R \)

3. **Substitute the Values into the Formula**: Replace \( \theta \) with \( P \) in the formula:
\[ \text{Area of sector} = \frac{P}{360} \times \pi R^2 \]

4. **Final Expression**: Thus, the area of the sector of angle \( P \) in degrees of a circle with radius \( R \) is:
\[ \text{Area of sector} = \frac{P \pi R^2}{360} \]

### Final Answer:
The area of the sector is given by:
\[ \text{Area} = \frac{P \pi R^2}{360} \]