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? Response area

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 Response area

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Answer 1

Certainly! Let's go through each of the steps together.

### Step 1: What is the formula for finding the area of a circle?
The formula for the area \( A \) of a circle is given by:
\[
A = \pi r^2
\]
where \( r \) is the radius of the circle and \( \pi \) is approximately 3.14.

### Step 2: What would be the first step in solving for the radius?
The first step in solving for the radius is to rearrange the formula to solve for \( r \). You can do this by dividing both sides by \( \pi \):
\[
r^2 = \frac{A}{\pi}
\]

### Step 3: What would be the second step in solving for the radius?
The second step is to take the square root of both sides to solve for \( r \):
\[
r = \sqrt{\frac{A}{\pi}}
\]

### Step 4: The approximate radius would be about
Given that the area \( A \) is approximately 45 square feet, we can substitute that value into the rearranged formula:
\[
r \approx \sqrt{\frac{45}{\pi}}
\]
Using \( \pi \approx 3.14 \):
\[
r \approx \sqrt{\frac{45}{3.14}} \approx \sqrt{14.33} \approx 3.79 \text{ feet}
\]

So, a good estimation for the radius of the circle would be about **3.8 feet**.