Final answer:
To find the square footage of the sandbox after the flower bed is installed, subtract the area of the circular flower bed from the total area of the sandbox. The resulting area is 77 square feet of sand.
Step-by-step explanation:
To find the square footage of the sandbox after the flower bed is installed, we need to subtract the area of the circular flower bed from the total area of the sandbox. First, let's find the area of the sandbox. The sandbox is 7 feet wide and 11 feet long, so the area of the sandbox is 7 feet x 11 feet = 77 square feet.
Next, let's find the area of the circular flower bed. Since the flower bed is circular, we can use the formula for the area of a circle: A = pi * r^2. The flower bed is 6 inches wide, which is 0.5 feet. So, the radius of the flower bed is 0.5 feet / 2 = 0.25 feet. Now we can calculate the area of the flower bed: A = 3.14 * (0.25 feet)^2 = 0.19625 square feet.
Finally, we subtract the area of the flower bed from the area of the sandbox to find the remaining area for sand: 77 square feet - 0.19625 square feet = 76.80375 square feet. Rounding to the nearest foot, there will be 77 square feet of sand after the flower bed is installed.