Question

Megan's gas fireplace uses propane. The liquid propane is stored in a spherical tank. The tank has a radius of 1 foot, 6 inches. The tank contains 7,741,000 Btu of energy when it is filled to 80% of its total volume. How much energy does 1 gallon of liquid propane in the tank contain?

Hint: There are exactly 231 cubic inches in 1 gallon.
If necessary, round your answer to the nearest hundred.

Answer 1

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.