The morning inspection of the tank farm finds a leak in the turpentine tank. The leak is repaired. An investigation finds that the leak was 0.1 inches in diameter and 7 feet above the tank bottom. Records show that the turpentine level in the tank was 17.3 feet before the leak occurred and 13.0 feet after the leak was repaired. The tank diameter is 15 feet.

Determine the total amount of turpentine spilled.

The total volume of turpentine spilled is the difference in volume of the tank before and after the leak, calculated using the formula for the volume of a cylinder. In this case, approximately 6322.875 cubic feet of turpentine were spilled.

Explanation:

The total amount of turpentine spilled can be found by finding the volume of a cylinder which represents our tank. The volume (V) of a cylinder is given by the formula V = πr²h, with r being the radius and h being the height, and π estimated as 3.14.

Firstly, calculate the volume before the leak occurred. The radius of the tank is half of the diameter, so r is 15/2 = 7.5 ft. The height is the level of the turpentine, which was 17.3 ft.

Therefore, the volume before leakage is V = 3.14 * (7.5 ft)² * 17.3 ft = 24660.375 cubic feet.

Secondly, calculate the volume after the leak is repaired. The height now is 13.0 ft, hence the volume after leakage is V = 3.14 * (7.5 ft)² * 13.0 ft = 18337.5 cubic feet.

The total amount of turpentine spilled is the difference between these two volumes, which is 24660.375 - 18337.5 = 6322.875 cubic feet.

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