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 given its circumference, we can follow these steps:

### Step 1: Write the formula for the circumference of a circle.
The formula for the circumference \( C \) of a circle is given by:
\[ C = 2 \pi r \]
where \( r \) is the radius of the circle.

### Step 2: Set the circumference equal to the given value.
We are given that the circumference is \( 3 \) cm. Therefore, we can set up the equation:
\[ 2 \pi r = 3 \]

### Step 3: Solve for the radius \( r \).
To find the radius, we can rearrange the equation:
\[ r = \frac{3}{2 \pi} \]

### Step 4: Write the formula for the area of a circle.
The area \( A \) of a circle is given by:
\[ A = \pi r^2 \]

### Step 5: Substitute the value of \( r \) into the area formula.
Now we substitute \( r = \frac{3}{2 \pi} \) into the area formula:
\[ A = \pi \left(\frac{3}{2 \pi}\right)^2 \]

### Step 6: Simplify the expression.
Calculating \( \left(\frac{3}{2 \pi}\right)^2 \):
\[ \left(\frac{3}{2 \pi}\right)^2 = \frac{9}{4 \pi^2} \]
Now substituting this back into the area formula:
\[ A = \pi \cdot \frac{9}{4 \pi^2} \]

### Step 7: Cancel out \( \pi \) and simplify further.
\[ A = \frac{9}{4 \pi} \]

### Final Answer:
Thus, the area of the circle is:
\[ A = \frac{9}{4} \pi \, \text{cm}^2 \]