Answer: To find the area of the ring-shaped path, we need to subtract the area of the inner circle (the pool) from the area of the outer circle. The radius of the pool is half the diameter, so it is 11 yards. The radius of the outer circle is the sum of the radius of the pool and the width of the path, so it is 11 + 5 = 16 yards.
The area of the pool is:
A_pool = pi * r^2 = pi * 11^2 ≈ 380.13 square yards
The area of the outer circle is:
A_outer = pi * R^2 = pi * 16^2 ≈ 804.25 square yards
The area of the ring-shaped path is:
A_path = A_outer - A_pool ≈ 804.25 - 380.13 ≈ 424.12 square yards
Since one gallon of coating can cover 5 square yards, we need:
Gallons = A_path / 5 ≈ 424.12 / 5 ≈ 84.82
Therefore, we need approximately 85 gallons of coating to cover the ring-shaped path.
Explanation: