Answer :
To find the area of the path surrounding the circular garden, we need to follow these steps:
1. Calculate the radius of the garden and the path combined:
- The radius of the garden is given as 8 feet.
- The width of the path is given as 3 feet.
- Therefore, the total radius (garden plus 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 garden:
- The area of a circle is given by the formula:
[tex]\[ \text{Area} = \pi \times (\text{radius})^2 \][/tex]
- For the garden with a radius of 8 feet:
[tex]\[ \text{Area of the garden} = \pi \times (8 \text{ feet})^2 = 3.14 \times 64 \text{ ft}^2 = 200.96 \text{ ft}^2 \][/tex]
3. Calculate the area of the garden plus the path:
- For the combined radius of 11 feet:
[tex]\[ \text{Area of the garden plus path} = \pi \times (11 \text{ feet})^2 = 3.14 \times 121 \text{ ft}^2 = 379.94 \text{ ft}^2 \][/tex]
4. Calculate the area of the path alone:
- The area of the path is given by the difference between the total area (garden plus path) and the area of the garden:
[tex]\[ \text{Area of the path} = \text{Area of the garden plus path} - \text{Area of the garden} = 379.94 \text{ ft}^2 - 200.96 \text{ ft}^2 = 178.98 \text{ ft}^2 \][/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]
1. Calculate the radius of the garden and the path combined:
- The radius of the garden is given as 8 feet.
- The width of the path is given as 3 feet.
- Therefore, the total radius (garden plus 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 garden:
- The area of a circle is given by the formula:
[tex]\[ \text{Area} = \pi \times (\text{radius})^2 \][/tex]
- For the garden with a radius of 8 feet:
[tex]\[ \text{Area of the garden} = \pi \times (8 \text{ feet})^2 = 3.14 \times 64 \text{ ft}^2 = 200.96 \text{ ft}^2 \][/tex]
3. Calculate the area of the garden plus the path:
- For the combined radius of 11 feet:
[tex]\[ \text{Area of the garden plus path} = \pi \times (11 \text{ feet})^2 = 3.14 \times 121 \text{ ft}^2 = 379.94 \text{ ft}^2 \][/tex]
4. Calculate the area of the path alone:
- The area of the path is given by the difference between the total area (garden plus path) and the area of the garden:
[tex]\[ \text{Area of the path} = \text{Area of the garden plus path} - \text{Area of the garden} = 379.94 \text{ ft}^2 - 200.96 \text{ ft}^2 = 178.98 \text{ ft}^2 \][/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]
