Final answer:
The cylindrical tank, which is 18 feet high with a diameter of 8.5 feet, can hold approximately 7633.36 gallons when filled to the top using the volume formula for a cylinder and converting the result from cubic feet to gallons.
Step-by-step explanation:
To calculate the volume of the cylindrical tank, we use the formula for the volume of a cylinder, which is V = πr^2h, where π is Pi (approximately 3.14159), r is the radius of the cylinder, and h is the height of the cylinder. Since the diameter of the tank is 8.5 feet, the radius is half of that, which is 4.25 feet. The height of the tank is given as 18 feet. So, the volume in cubic feet is:
V = π * (4.25 feet)^2 * 18 feet
V = 3.14159 * 18.0625 * 18
V = 3.14159 * 325.125
V ≈ 1021.52 cubic feet
Next, to convert cubic feet to gallons, we use the conversion factor that 1 cubic foot is equivalent to approximately 7.48 gallons:
1021.52 cubic feet * 7.48 gallons/cubic foot ≈ 7633.36 gallons.
Therefore, the cylindrical tank can hold approximately 7633.36 gallons when filled to the top.