If the numerical value of the circumference and area of a circle is same, then the area is

Options

A. `6pi` sq. unit
B. `4 pi` sq. unit
C. `8 pi` sq. unit
D. `12 pi` sq. unit

Answer

To solve the problem, we need to find the area of a circle when the numerical values of its circumference and area are equal.

### Step-by-Step Solution:

1. **Understand the formulas**:
- The formula for the circumference (C) of a circle is given by:
\[ C = 2 \pi r \]
- The formula for the area (A) of a circle is given by:
\[ A = \pi r^2 \]

2. **Set the circumference equal to the area**:
Since the problem states that the numerical values of the circumference and area are the same, we can set the two equations equal to each other:
\[ 2 \pi r = \pi r^2 \]

3. **Simplify the equation**:
We can divide both sides of the equation by \(\pi\) (assuming \(\pi \neq 0\)):
\[ 2r = r^2 \]

4. **Rearrange the equation**:
Rearranging gives us:
\[ r^2 - 2r = 0 \]

5. **Factor the equation**:
Factoring out \(r\) gives:
\[ r(r - 2) = 0 \]

6. **Solve for \(r\)**:
This gives us two solutions:
\[ r = 0 \quad \text{or} \quad r = 2 \]
Since \(r = 0\) does not represent a valid circle, we take \(r = 2\).

7. **Calculate the area**:
Now that we have the radius, we can find the area:
\[ A = \pi r^2 = \pi (2)^2 = 4\pi \]

### Conclusion:
Thus, the area of the circle is \(4\pi\) square units.