Final answer:
To find out how many gallons a 186 ft diameter spherical fuel tank holds, calculate its volume using the sphere volume formula and then convert cubic feet to gallons using the provided conversion factor of 1 ft3 ≈ 7.5 gal.
Step-by-step explanation:
To calculate the number of gallons a spherical fuel tank holds when it is 186 ft in diameter, we first determine its volume. The volume V of a sphere is given by the formula V = (4/3)πr3, where r is the radius of the sphere. Since the diameter is 186 feet, the radius r is 186 / 2 = 93 ft. So, the volume of the sphere is:
V = (4/3)π(93 ft)3
Next, we need to convert cubic feet to gallons using the given conversion: 1 ft3 ≈ 7.5 gal. First, calculate the volume in cubic feet, then multiply by the conversion factor to get the volume in gallons.
The number of gallons g is:
g = volume in ft3 × 7.5 gal/ft3
We can now calculate and find out how many gallons of fuel the tank can hold.