If the magnitude of the area of a circle is equal to its circumference in cm, the diameter of the cirlce is

Options

A. 2 cms
B. 4 cms
C. 1 cms
D. `pi ` cms

Answer

To solve the problem where the area of a circle is equal to its circumference, we can follow these steps:

### Step-by-Step Solution:

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

2. **Set the area equal to the circumference**:
According to the problem, the area is equal to the circumference:
\[ \pi r^2 = 2\pi r \]

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

4. **Rearrange the equation**:
To solve for \( r \), we can rearrange the equation:
\[ r^2 - 2r = 0 \]

5. **Factor the equation**:
We can factor out \( r \):
\[ r(r - 2) = 0 \]

6. **Find the values of \( r \)**:
Setting each factor to zero gives us:
\[ r = 0 \quad \text{or} \quad r = 2 \]
Since \( r = 0 \) does not make sense in the context of a circle, we take \( r = 2 \).

7. **Calculate the diameter**:
The diameter \( d \) of a circle is given by:
\[ d = 2r \]
Substituting the value of \( r \):
\[ d = 2 \times 2 = 4 \text{ cm} \]

### Final Answer:
The diameter of the circle is \( 4 \) cm.

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