Let's solve the problem step-by-step.
1. Calculate the radius of the outer circle (garden + path):
- The radius of the garden is [tex]\(8\)[/tex] feet.
- The width of the path is [tex]\(3\)[/tex] feet.
- Therefore, the radius of the outer circle, which includes both the garden and the path, is:
[tex]\[
\text{radius\_outer} = \text{radius\_garden} + \text{width\_path} = 8 \, \text{feet} + 3 \, \text{feet} = 11 \, \text{feet}
\][/tex]
2. Calculate the area of the outer circle:
- The formula for the area of a circle is [tex]\(A = \pi r^2\)[/tex], where [tex]\(r\)[/tex] is the radius.
- Using [tex]\( \pi = 3.14 \)[/tex] and [tex]\( \text{radius\_outer} = 11 \)[/tex] feet:
[tex]\[
\text{area\_outer} = 3.14 \times (11 \, \text{feet})^2 = 3.14 \times 121 = 379.94 \, \text{square feet}
\][/tex]
3. Calculate the area of the inner garden circle:
- Again, using the formula [tex]\(A = \pi r^2\)[/tex] and [tex]\( \text{radius\_garden} = 8 \)[/tex] feet:
[tex]\[
\text{area\_garden} = 3.14 \times (8 \, \text{feet})^2 = 3.14 \times 64 = 200.96 \, \text{square feet}
\][/tex]
4. Calculate the area of the path alone:
- The area of the path is the difference between the area of the outer circle and the area of the inner garden circle:
[tex]\[
\text{area\_path} = \text{area\_outer} - \text{area\_garden} = 379.94 \, \text{square feet} - 200.96 \, \text{square feet} = 178.98 \, \text{square feet}
\][/tex]
Thus, the approximate area of the path alone is [tex]\(\boxed{178.98 \, \text{square feet}}\)[/tex].
