IF the circumference of a circular plate is `12pi` units, what would be its area ?

Answer

To find the area of a circular plate given its circumference, we can follow these steps:

### Step-by-Step Solution:

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

2. **Set up the equation with the given circumference**:
We are given that the circumference of the circular plate is \( 12\pi \) units. Therefore, we can set up the equation:
\[ 2\pi r = 12\pi \]

3. **Solve for the radius \( r \)**:
To find \( r \), we can divide both sides of the equation by \( 2\pi \):
\[ r = \frac{12\pi}{2\pi} \]
Simplifying this gives:
\[ r = \frac{12}{2} = 6 \text{ units} \]

4. **Use the radius to find the area**:
The area \( A \) of a circle is given by the formula:
\[ A = \pi r^2 \]
Now substituting the value of \( r \) we found:
\[ A = \pi (6)^2 \]

5. **Calculate the area**:
Simplifying further:
\[ A = \pi \times 36 = 36\pi \text{ square units} \]

### Final Answer:
The area of the circular plate is \( 36\pi \) square units.

---