Question

If you have a circle with an area of approximately 45 square feet, what is a good estimation for the radius of the circle?(4 points)

Step 1: What is the formula for finding the area of a circle?

Step 2: What would be the first step in solving for the radius? Response area

Step 3: What would be the second step in solving for the radius? Response area

Step 4: The approximate radius would be about

responcese:
Take the square root of each side of the equation.
Multiply by 2 on each side of the equation.
Subtract π from each side of the equation.
Square each side of the equation.
Divide by π on each side of the equation.
Divide by 2 on each side of the equation.
205 feet
A = 2πr^(3)
7.16 feet
A = 2πr^(2)
2.1feet
C = 2πr
3.8 feet

Answer 1

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:
1. First, approximate \( \pi \approx 3.14 \).
2. Thus, \( \frac{45}{\pi} \approx \frac{45}{3.14} \approx 14.32 \).
3. 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).