To find the approximate area of the path alone, we need to determine the areas of the garden and the total area of the garden plus the path, then subtract the area of the garden from the total area. Here's a step-by-step solution:
1. Calculate the area of the garden:
- The radius of the garden is 8 feet.
- The formula for the area of a circle is [tex]\( \pi r^2 \)[/tex].
- Substituting the given values: [tex]\( \pi \approx 3.14 \)[/tex] and [tex]\( r = 8 \)[/tex] feet.
[tex]\[
\text{Area of the garden} = 3.14 \times (8^2) = 3.14 \times 64 = 200.96 \text{ square feet}
\][/tex]
2. Calculate the total radius including the path:
- The width of the path is 3 feet.
- The total radius (garden + path) is [tex]\( 8 + 3 = 11 \)[/tex] feet.
3. Calculate the total area of the garden including the path:
- Using the radius of 11 feet.
[tex]\[
\text{Total Area} = 3.14 \times (11^2) = 3.14 \times 121 = 379.94 \text{ square feet}
\][/tex]
4. Calculate the area of the path alone:
- Subtracting the area of the garden from the total area.
[tex]\[
\text{Area of the path} = 379.94 \text{ square feet} - 200.96 \text{ square feet} = 178.98 \text{ square feet}
\][/tex]
Hence, the approximate area of the path alone is:
[tex]\[
\boxed{178.98 \text{ square feet}}
\][/tex]
