If the area and circumference of a circle are numerically equal, then the radius of circle is_____.

Options

A. 2 units
B. 4 units
C. `pi` units
D. 6 units

Answer

To solve the problem where the area and circumference of a circle are numerically equal, we can follow these steps:

1. **Write down the formulas for area and circumference of a circle.**
- 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 and circumference are equal:
\[ \pi r^2 = 2\pi r \]

3. **Cancel out the common terms.**
- 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. **Solve for \( r \).**
- Setting each factor to zero gives us:
\[ r = 0 \quad \text{or} \quad r - 2 = 0 \]
- Thus, we find:
\[ r = 0 \quad \text{or} \quad r = 2 \]

7. **Determine the valid solution.**
- Since a radius cannot be negative or zero in the context of a circle, we take:
\[ r = 2 \]

Therefore, the radius of the circle is \( \boxed{2} \).