Problems with Cylindrical Tanks
Molly McKee
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?
Begin by calculating the area of the sector and then subtract away the area of the triangle.
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Half of the chord:
Area of the triangle:
The volume of the tank:
V = 15552π, or about 48858 cubic inches
(1 cubic inch = 0.0043 gallons)
Therefore, the tank holds approximately 210 gallons
359.63 - 129 = 230.63 in2
(230.63 in2)(48 in) = 11070.24 in3
The tank has approximately 47.6 gallons in it.
This is enough oil for the Superintendent to finish the season.