If the circumference of a circle is 3 cm, then its area, in `cm^(2)`, is

Options

A. `(9pi)/(4)`
B. `(3pi)/(2)`
C. `(9)/(4pi)`
D. `(4)/(9pi)`

Answer

To find the area of a circle when its circumference is given, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the given information**:
The circumference of the circle is given as 3 cm.

2. **Use the formula for circumference**:
The formula for the circumference (C) of a circle is:
\[ C = 2\pi r \]
where \( r \) is the radius of the circle.

3. **Set up the equation**:
Substitute the given circumference into the formula:
\[ 3 = 2\pi r \]

4. **Solve for the radius \( r \)**:
Rearranging the equation to isolate \( r \):
\[ r = \frac{3}{2\pi} \]

5. **Use the formula for area**:
The area (A) of a circle is given by:
\[ A = \pi r^2 \]

6. **Substitute the radius into the area formula**:
Substitute \( r = \frac{3}{2\pi} \) into the area formula:
\[ A = \pi \left(\frac{3}{2\pi}\right)^2 \]

7. **Calculate \( r^2 \)**:
\[ A = \pi \cdot \frac{9}{4\pi^2} \]

8. **Simplify the expression**:
\[ A = \frac{9\pi}{4\pi^2} \]
Cancel out one \( \pi \):
\[ A = \frac{9}{4\pi} \text{ cm}^2 \]

### Final Answer:
The area of the circle is \( \frac{9}{4\pi} \) cm².