Answer: To find the area of the 7-ft-wide walk surrounding the pool, we need to calculate the total area of the outer region and then subtract the area of the pool itself.
The pool is in the form of a semicircular-sided figure, and its width is 16 ft. This means the radius of the pool is half of the width, which is 16 ft / 2 = 8 ft.
Calculate the area of the pool:
The pool is a semicircle, and its area is given by A_pool = (1/2) * π * r^2, where r is the radius.
A_pool = (1/2) * π * 8^2
A_pool = (1/2) * π * 64
A_pool = 32π square feet
Calculate the total area of the outer region (including the walk):
The total width of the outer region is the width of the pool (16 ft) + 2 times the width of the walk (7 ft), which is 16 ft + 2 * 7 ft = 16 ft + 14 ft = 30 ft.
Since the outer region is a rectangle (with a semicircle on top), its area is given by A_outer = length * width.
The length of the outer region is the diameter of the pool, which is twice the radius, so it is 2 * 8 ft = 16 ft.
A_outer = 16 ft * 30 ft
A_outer = 480 square feet
Find the area of the walk by subtracting the area of the pool from the total area of the outer region:
A_walk = A_outer - A_pool
A_walk = 480 square feet - 32π square feet
Now, we need to approximate the value of π (pi) to calculate the area of the walk. Let's use π ≈ 3.14.
A_walk ≈ 480 square feet - 32 * 3.14 square feet
A_walk ≈ 480 square feet - 100.48 square feet
A_walk ≈ 379.52 square feet
The area of the 7-ft-wide walk surrounding the pool is approximately 379.52 square feet.