To solve the problem of finding the approximate area of the path alone, let's follow these steps:
1. Determine the total radius: The radius of the garden is given as 8 feet. The path around the garden adds another 3 feet to this radius. Therefore, the total radius (from the center of the garden to the outer edge of the path) is:
[tex]\[
\text{Total radius} = \text{Radius of the garden} + \text{Width of the path} = 8\, \text{feet} + 3\, \text{feet} = 11\, \text{feet}
\][/tex]
2. Calculate the area of the larger circle (garden + path): Using the total radius of 11 feet, we can find the area of the larger circle. The formula for the area of a circle is [tex]\( \pi r^2 \)[/tex]:
[tex]\[
\text{Area of the larger circle} = \pi \times (11\, \text{feet})^2 = 3.14 \times 121\, \text{feet}^2 = 379.94\, \text{feet}^2
\][/tex]
3. Calculate the area of the garden alone: Next, we use the radius of just the garden, which is 8 feet, to calculate the area of the garden alone:
[tex]\[
\text{Area of the garden} = \pi \times (8\, \text{feet})^2 = 3.14 \times 64\, \text{feet}^2 = 200.96\, \text{feet}^2
\][/tex]
4. Calculate the area of the path alone: The area of the path is the difference between the area of the larger circle (garden + path) and the area of the garden:
[tex]\[
\text{Area of the path} = \text{Area of larger circle} - \text{Area of garden} = 379.94\, \text{feet}^2 - 200.96\, \text{feet}^2 = 178.98\, \text{feet}^2
\][/tex]
Therefore, the approximate area of the path alone is [tex]\( 178.98 \, \text{ft}^2 \)[/tex]. The correct answer is:
[tex]\[
\boxed{178.98 \, \text{ft}^2}
\][/tex]
