To determine the difference in the areas of two circles given their diameters, let's follow these steps:
1. Calculate the radius of both circles
- The diameter of the first circle is 4 meters. The radius (r1) is half of the diameter:
[tex]\[
r1 = \frac{4}{2} = 2 \text{ meters}
\][/tex]
- The diameter of the second circle is 6 meters. The radius (r2) is half of the diameter:
[tex]\[
r2 = \frac{6}{2} = 3 \text{ meters}
\][/tex]
2. Calculate the area of both circles
- The formula to calculate the area of a circle is [tex]\( A = \pi r^2 \)[/tex].
- For the first circle with radius 2 meters:
[tex]\[
A1 = \pi \times (2)^2 = \pi \times 4 \approx 12.57 \text{ square meters}
\][/tex]
- For the second circle with radius 3 meters:
[tex]\[
A2 = \pi \times (3)^2 = \pi \times 9 \approx 28.27 \text{ square meters}
\][/tex]
3. Calculate the difference in areas
- Subtract the area of the first circle from the area of the second circle:
[tex]\[
\text{Difference} = A2 - A1 \approx 28.27 - 12.57 = 15.71 \text{ square meters}
\][/tex]
4. Round the result to the nearest square meter
- The difference in areas is approximately 15.71 square meters. When rounded to the nearest square meter, this is:
[tex]\[
\approx 16 \text{ square meters}
\][/tex]
Therefore, the difference in the areas of a circle with a diameter of 4 meters and a circle with a diameter of 6 meters, rounded to the nearest square meter, is:
[tex]\[
\boxed{16 \, \text{m}^2}
\][/tex]
