`("Area of a sector")/("Area of a circle ")= `

Options

A. `theta/180`
B. `theta/360`
C. `180/theta
D. `360/theta`

Answer

To find the ratio of the area of a sector to the area of a circle, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the formulas**:
- The area of a sector of a circle is given by 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.
- The area of a circle is given by the formula:
\[ \text{Area of Circle} = \pi r^2 \]

2. **Write the ratio**:
- We need to find the ratio of the area of the sector to the area of the circle:
\[ \frac{\text{Area of Sector}}{\text{Area of Circle}} = \frac{\frac{\theta}{360} \times \pi r^2}{\pi r^2} \]

3. **Simplify the ratio**:
- In the above expression, \(\pi r^2\) in the numerator and denominator will cancel out:
\[ \frac{\text{Area of Sector}}{\text{Area of Circle}} = \frac{\theta}{360} \]

4. **Final result**:
- Therefore, the ratio of the area of the sector to the area of the circle is:
\[ \frac{\text{Area of Sector}}{\text{Area of Circle}} = \frac{\theta}{360} \]