The boilers in a boiler installation consume 780 gallons per hour. The fuel oil storage tank is a vertical cylinder 18 feet in diameter and currently contains oil to a depth of 14.5 feet. At the current consumption rate, approximately how many hours will the supply last?

The boilers in a boiler installation consume 780 gallons per hour. The fuel oil storage tank is a vertical cylinder 18 feet in diameter and currently contains oil to a depth of 14.5 feet. At the current consumption rate, approximately how many hours will the supply last?

• A. 30.2 Hours
• B. 40.1 Hours
• C. 28.7 Hours
• D. 35.4 Hours

Answer: (D)

Calculating how long the oil lasts comes down to finding the tank’s volume and then dividing by the consumption rate. For a vertical cylinder, volume equals the base area times the oil depth. The base radius is half the diameter, so here r = 9 ft. The base area is πr^2 = π(9^2) = 81π ft^2 ≈ 254.47 ft^2. With a depth of 14.5 ft, the oil volume is 254.47 × 14.5 ≈ 3,689.8 cubic feet. Converting to gallons using 1 ft^3 ≈ 7.48052 gallons gives about 3,689.8 × 7.48052 ≈ 27,602 gallons. At a consumption rate of 780 gallons per hour, the duration is 27,602 ÷ 780 ≈ 35.4 hours. So the supply will last about 35.4 hours.