To solve for the area of the walk surrounding the circular fountain, you need to first calculate the area of the fountain itself and then the area of the larger circle that includes the walk.
1. **Calculate the radius of the fountain**: The fountain has a diameter of 10 feet, so the radius (r) of the fountain is:
r = diameter / 2 = 10 feet / 2 = 5 feet
2. **Identify the outer radius of the circular walk**: Since the walk is 3 feet wide, you need to add this width to the radius of the fountain:
Outer radius = fountain radius + width of walk = 5 feet + 3 feet = 8 feet
3. **Calculate the area of the fountain**: The area (Afountain) of a circle is calculated using the formula:
Afountain = π * (radius2)
Substituting the fountain’s radius:
Afountain = π * (5 feet)2 = 25π square feet
4. **Calculate the area of the larger circle**: Now, use the outer radius to find the area (Atotal) of the circle that includes both the fountain and the walk:
Atotal = π * (8 feet)2 = 64π square feet
5. **Determining the area of the walk**: To find the area of the walk alone, subtract the area of the fountain from the area of the larger circle:
Area of the walk = Atotal – Afountain = 64π – 25π = 39π square feet
6. **Final Calculation**: If you calculate this using π ≈ 3.14, the area of the walk is:
Area of the walk ≈ 39 * 3.14 ≈ 122.86 square feet
Thus, the area of the walk surrounding the fountain is approximately 122.86 square feet.