A fuel oil settler is 35 feet 4 inches (10.7696 m) long, 25 feet 10 inches ( 7.8740 m) wide, and 19 feet (5.7912 m) deep. The noon sounding indicated a level of 15 feet 2 inches (4.6228 m). The fuel oil meter read 6517 gal. (24669) at that time and 8911 gal. (33732) at 1600. How many barrels / cubic meters of fuel oil remained in the settler at 1600?
• Volume of a rectangular tank = length × breadth × observed depth of liquid • Relationship between gallons, barrels, and cubic meters (unit conversions) • How to use a difference in meter readings to find how much fuel was consumed between two times
• First, if the tank is a simple box, what is the volume corresponding to the actual liquid depth at 1600, not at noon? How might you find that depth using the given meter readings? • How many gallons were on board at noon if you know both the tank geometry and the sounding? Then, how many gallons remain at 1600 if you know how much was used? • After you find the remaining gallons, which conversions do you need to apply to express that quantity in both barrels and cubic meters, and which option is of the right order of magnitude for such a tank size?
• Be sure you are using the change in the meter reading (1600 minus noon) to find fuel used, not the absolute values directly as the answer. • Check that your tank volume calculation uses consistent units (all in feet or all in meters) before converting to gallons. • Verify your unit conversions: gallons-to-barrels (42 gal per bbl) and gallons-to-cubic-meters (about 264.172 gallons per cubic meter).
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