To approximate the area of a circle with a given radius, we will follow these steps:
1. Identify the formula for the area of a circle:
The formula for the area \( A \) of a circle is given by:
[tex]\[
A = \pi r^2
\][/tex]
where \( \pi \) is a constant approximately equal to 3.14, and \( r \) is the radius of the circle.
2. Substitute the given values into the formula:
Given:
[tex]\[
r = 2.2 \, \text{m}
\][/tex]
Using \( \pi \approx 3.14 \), we substitute these values into the formula:
[tex]\[
A = 3.14 \times (2.2)^2
\][/tex]
3. Calculate the square of the radius:
[tex]\[
(2.2)^2 = 2.2 \times 2.2 = 4.84
\][/tex]
4. Multiply by \(\pi\) to find the area:
[tex]\[
A = 3.14 \times 4.84
\][/tex]
When multiplying these values, we get:
[tex]\[
A \approx 15.1976 \, \text{m}^2
\][/tex]
5. Round the result to the nearest tenth:
To round \( 15.1976 \) to the nearest tenth, we look at the digit in the hundredths place (9). Since it is 5 or greater, we round up the tenths place.
[tex]\[
15.1976 \approx 15.2
\][/tex]
Therefore, the approximate area of the circle is:
[tex]\[
A \approx 15.2 \, \text{m}^2
\][/tex]
