For a circle having radius r, what is the area of quadrant?

Options

A. `(pir)/2`
B. `(pir^2+2r)`
C. `1/4pir^2`
D. `1/2pir^2`

Answer

To find the area of a quadrant of a circle with radius \( r \), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Circle and Quadrant**:
A circle can be divided into four equal parts, known as quadrants. Each quadrant represents one-fourth of the entire circle.

2. **Formula for Area of a Circle**:
The area \( A \) of a circle is given by the formula:
\[ A = \pi r^2 \]
where \( r \) is the radius of the circle.

3. **Calculate the Area of the Quadrant**:
Since a quadrant is one-fourth of the circle, we can find the area of the quadrant by dividing the area of the circle by 4:
\[ \text{Area of Quadrant} = \frac{1}{4} \times A = \frac{1}{4} \times \pi r^2 \]

4. **Simplify the Expression**:
This can be simplified to:
\[ \text{Area of Quadrant} = \frac{\pi r^2}{4} \]

### Final Answer:
The area of the quadrant of a circle with radius \( r \) is:
\[ \frac{\pi r^2}{4} \]