If diameter of a circle is `( r )/( 2) cm `, Then the area of a circle is `:`

Options

A. `pi r^(2) cm^(2)`
B. `( pi r^(2))/( 16) cm^(2)`
C. `( pi r^(2))/( 4) cm^(2)`
D. `pi r cm^(2)`

Answer

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

### Step-by-Step Solution:

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

2. **Calculate the Radius**:
The radius \( r \) of the circle is half of the diameter. Therefore, we can calculate the radius as:
\[ r = \frac{D}{2} = \frac{\frac{r}{2}}{2} = \frac{r}{4} \text{ cm} \]

3. **Use the Area Formula**:
The area \( A \) of a circle is given by the formula:
\[ A = \pi r^2 \]
Substituting the value of the radius we found:
\[ A = \pi \left(\frac{r}{4}\right)^2 \]

4. **Simplify the Area Expression**:
Now we simplify the expression:
\[ A = \pi \left(\frac{r^2}{16}\right) = \frac{\pi r^2}{16} \]

5. **Final Result**:
Therefore, the area of the circle is:
\[ A = \frac{\pi r^2}{16} \text{ cm}^2 \]