The area of a circle of radius 5 is numerically what percent of its circumference ?

Options

A. `200%`
B. `225%`
C. `240%`
D. `250%`

Answer

To solve the problem, we need to find the area and circumference of a circle with a radius of 5, and then determine what percentage the area is of the circumference.

### Step-by-Step Solution:

1. **Calculate the Area of the Circle:**
The formula for the area \( A \) of a circle is given by:
\[ A = \pi r^2 \]
Substituting the radius \( r = 5 \):
\[ A = \pi (5)^2 = \pi \times 25 = 25\pi \]

2. **Calculate the Circumference of the Circle:**
The formula for the circumference \( C \) of a circle is given by:
\[ C = 2\pi r \]
Substituting the radius \( r = 5 \):
\[ C = 2\pi (5) = 10\pi \]

3. **Find the Percentage of the Area with respect to the Circumference:**
To find what percent the area is of the circumference, we use the formula:
\[ \text{Percentage} = \left( \frac{\text{Area}}{\text{Circumference}} \right) \times 100 \]
Substituting the values we calculated:
\[ \text{Percentage} = \left( \frac{25\pi}{10\pi} \right) \times 100 \]
The \( \pi \) cancels out:
\[ \text{Percentage} = \left( \frac{25}{10} \right) \times 100 = 2.5 \times 100 = 250 \]

4. **Final Answer:**
The area of the circle of radius 5 is numerically 250% of its circumference.