To determine the approximate area of the path alone, we need to perform a series of calculations.
Step 1: Determine the radius of the garden.
The radius of the garden is given as 8 feet.
Step 2: Determine the width of the path surrounding the garden.
The width of the path is given as 3 feet.
Step 3: Calculate the radius of the outer boundary (the garden plus the path).
The radius of the outer circle (garden plus path) is found by adding the width of the path to the radius of the garden:
[tex]\[ \text{Radius of the outer circle} = 8 \text{ feet} + 3 \text{ feet} = 11 \text{ feet} \][/tex]
Step 4: Calculate the area of the garden using the formula for the area of a circle, [tex]\( A = \pi r^2 \)[/tex].
[tex]\[ \text{Area of the garden} = \pi \times (8 \text{ feet})^2 \approx 3.14 \times 64 \approx 200.96 \text{ square feet} \][/tex]
Step 5: Calculate the area of the outer circle using the same formula.
[tex]\[ \text{Area of the outer circle} = \pi \times (11 \text{ feet})^2 \approx 3.14 \times 121 \approx 379.94 \text{ square feet} \][/tex]
Step 6: Determine the area of the path alone by subtracting the area of the garden from the area of the outer circle.
[tex]\[ \text{Area of the path} = \text{Area of the outer circle} - \text{Area of the garden} \approx 379.94 \text{ square feet} - 200.96 \text{ square feet} \approx 178.98 \text{ square feet} \][/tex]
So, the approximate area of the path alone is:
[tex]\[ 178.98 \, \text{square feet} \][/tex]
Therefore, the correct answer is:
[tex]\[ \boxed{178.98 \, \text{ft}^2} \][/tex]
