In this set we want to consider the problem context of the storage of fluids in cylindrical tanks that have been installed laying on their side. The common problem characteristic is that the DEPTH of the fluid is known, determine the volume.
First Situation
This problem was seriously proposed to one of my EMT 725 students by their Superintendent. At the Superintendent's home the furnace used fuel oil stored in an underground tank. It was known that the tank was installed level on its side and that it was 36 inches in diameter and 48 inches long. Using a stick dipped through the fill tube, the superintendent determined he had 10 inches of oil in the tank. He really did NOT want to know how to calculate the amount of oil. He knew from experience that it was February and he would need about 40 gallons of oil to finish the season. Would he have enough oil?
An estimate may suffice. For example, the surface of the oil is a rectangle 48 incles long and a little less than 18 incles wide. So the volume would be less than 48 X 36 X 10 cubic inches. This is the volume of rectangular parallelepiped. At 231 cubic incles per gallon, this given an overestimate of 75 gallons. In fact if we approximate the oil in the tank by a trianglular prism with altitude of 10 and base of 36 and lenght of 48 its volume is half of this parallelepiped, or 37.5 gallons estimated. That estimate is probably pretty close, but who would want to assure their boss that he has enough oil in the tank to finish out the winter on the basis of this estimate?
We may want to calculate the volume.
