If diameter of a circle is 2r cm, then area of the circle is `:`

Options

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

Answer

To find the area of a circle when the diameter is given as \(2r\) cm, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Diameter**: The diameter of the circle is given as \(2r\) cm.

2. **Calculate the Radius**: The radius \(r\) is half of the diameter. Therefore, we can calculate the radius as:
\[ \text{Radius} = \frac{\text{Diameter}}{2} = \frac{2r}{2} = r \text{ cm} \]

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, we substitute the radius \(r\) into the area formula:
\[ A = \pi (r)^2 = \pi r^2 \]

5. **Final Result**: Therefore, the area of the circle when the diameter is \(2r\) cm is:
\[ A = \pi r^2 \text{ cm}^2 \]