Answer:
26 gallons
Explanation:
We need to find the area of the ring-shaped path in order to determine how many gallons of coating we need.
First, we need to find the radius of the inner circle:
Radius = diameter/2 = 14 yd/2 = 7 yd
Next, we need to find the radius of the outer circle:
Radius = diameter/2 = 18 yd/2 = 9 yd
Now we can find the area of the ring-shaped path by subtracting the area of the inner circle from the area of the outer circle:
Area = π(9^2) - π(7^2) = π(81) - π(49) = 32π
Since we know that one gallon of coating covers 4yd squared, we can divide the area of the path by 4 to find how many gallons we need:
32π/4 = 8π
This is approximately 25.13, but since we can only buy whole gallons of coating, we need to round up to the nearest gallon.
Therefore, we need 26 gallons of coating to cover the path.