Answer :
Final answer:
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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