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Answer :
Answer:
First, we need to find the total volume of the spherical tank. We can use the formula for the volume of a sphere:
V = (4/3)πr³
We are given that the radius is 1 foot, 6 inches, which is 1.5 feet.
V = (4/3)π(1.5)³
V ≈ 14.14 ft³
To find the volume of propane in the tank when it is filled to 80%, we multiply the total volume by 0.8:
V_propane = 0.8 × 14.14
V_propane ≈ 11.31 ft³
We are also given that the tank contains 7,741,000 Btu of energy. To find the energy per gallon, we need to know how many gallons are in the tank. One gallon is equal to 231 cubic inches.
1 ft³ = 12³ = 1,728 in³
11.31 ft³ = 11.31 × 1,728 in³
11.31 ft³ ≈ 19,536 in³
19,536 in³ ÷ 231 in³/gal ≈ 84.5 gallons
So, the tank contains approximately 84.5 gallons of propane. To find the energy per gallon, we divide the total energy by the number of gallons:
7,741,000 Btu ÷ 84.5 gal ≈ 91,580 Btu/gal
Therefore, 1 gallon of liquid propane in the tank contains approximately 91,580 Btu of energy.
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