To find the area of a circle given its diameter and round it to the nearest tenth, follow these steps:
1. Determine the diameter of the circle:
Given that the diameter of the circle is 13 meters.
2. Calculate the radius:
The radius is half of the diameter. So,
[tex]\[
\text{Radius} = \frac{\text{Diameter}}{2} = \frac{13}{2} = 6.5 \text{ meters}
\][/tex]
3. Use the formula for the area of a circle:
The formula to find the area [tex]\( A \)[/tex] of a circle is:
[tex]\[
A = \pi \times (\text{Radius})^2
\][/tex]
Substitute the radius into the formula:
[tex]\[
A = \pi \times (6.5)^2
\][/tex]
4. Calculate the area:
[tex]\[
A \approx 3.14159 \times 42.25 \approx 132.73228961416876 \text{ square meters}
\][/tex]
5. Round the area to the nearest tenth:
Looking at the value 132.73228961416876, you see that the digit in the tenths place is 7 (immediately following the decimal point is the number 132.7).
Therefore, the area of the circle, rounded to the nearest tenth, is:
[tex]\[
A \approx 132.7 \text{ square meters}
\][/tex]
Thus, the final answer is [tex]\(A = 132.7\)[/tex] square meters.
