Let's go through the steps to find an estimation for the radius of the circle with the given area of approximately 45 square feet.
Step 1: What is the formula for finding the area of a circle?
The formula for the area \( A \) of a circle is: \[ A = \pi r^2 \] where \( r \) is the radius of the circle.
Step 2: What would be the first step in solving for the radius?
To solve for the radius \( r \), the first step would be to rearrange the formula to isolate \( r^2 \): \[ r^2 = \frac{A}{\pi} \] In this case, since the area \( A \) is approximately 45 square feet, we would substitute that value.
Step 3: What would be the second step in solving for the radius?
The second step is to calculate \( r^2 \) using the rearranged formula: \[ r^2 = \frac{45}{\pi} \] Then you would compute this value.
Step 4: The approximate radius would be about
To find the radius \( r \), we would take the square root of both sides: \[ r = \sqrt{\frac{45}{\pi}} \]
Calculating this value:
- First, approximate \( \pi \approx 3.14 \).
- Thus, \( \frac{45}{\pi} \approx \frac{45}{3.14} \approx 14.32 \).
- Then, take the square root: \( r \approx \sqrt{14.32} \approx 3.78 \) feet.
So, the approximate radius of the circle would be about 3.8 feet (rounding to one decimal place).