If diameter of a circle is r cm, then the area of a circle is `:`

Options

A. `pi r^(2) cm^(2)`
B. `( pi r^(2))/( 4) cm^(2)`
C. `( pi r^(2))/( 2) cm^(2)`
D. `2 pi r cm^(2)`

Answer

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

### Step-by-Step Solution:

1. **Identify the Diameter**:
- Given that the diameter of the circle is \( r \) cm.

2. **Calculate the Radius**:
- The radius \( R \) of the circle is half of the diameter. Therefore,
\[ R = \frac{r}{2} \text{ cm} \]

3. **Use the Area Formula**:
- The formula for the area \( A \) of a circle is given by:
\[ A = \pi R^2 \]

4. **Substitute the Radius into the Area Formula**:
- Now substitute \( R \) with \( \frac{r}{2} \):
\[ A = \pi \left(\frac{r}{2}\right)^2 \]

5. **Simplify the Expression**:
- Squaring \( \frac{r}{2} \) gives:
\[ A = \pi \cdot \frac{r^2}{4} \]
- Thus, the area of the circle can be expressed as:
\[ A = \frac{\pi r^2}{4} \]

### Final Answer:
The area of the circle when the diameter is \( r \) cm is:
\[ A = \frac{\pi r^2}{4} \text{ cm}^2 \]