A swimming pool has a volume of 50,000 cubic feet. How many gallons of water does the pool hold?
The correct answer and explanation is:
To convert the volume of the swimming pool from cubic feet to gallons, you need to use the conversion factor between cubic feet and gallons.
1 cubic foot is equivalent to 7.48 gallons. Therefore, to find the number of gallons in 50,000 cubic feet, you multiply the volume in cubic feet by 7.48. Gallons=50,000 cubic feet×7.48 gallons/cubic foot\text{Gallons} = 50,000 \, \text{cubic feet} \times 7.48 \, \text{gallons/cubic foot} Gallons=374,000 gallons\text{Gallons} = 374,000 \, \text{gallons}
Thus, the swimming pool holds 374,000 gallons of water.
Explanation:
The conversion factor of 7.48 gallons per cubic foot is based on the fact that 1 gallon of water is defined as the amount of space that would occupy a cube with a side length of 7.48 inches. This is the standard unit conversion used for water volumes.
To better understand the process, consider that the gallon is a unit of volume used in the U.S. for liquids, while cubic feet is part of the imperial system of measurement, which is often used for large volumes such as pools.
To visualize, imagine a cubic box that has dimensions of 1 foot on each side. The space inside this box, the cubic foot, would contain 7.48 gallons of water. To determine the total amount of water a swimming pool can hold, you multiply the total volume of the pool in cubic feet by this conversion factor.
This process is a common method when needing to convert between volume units in various settings, including pools, tanks, or even fuel consumption. The accurate conversion ensures that the amount of water, or any liquid, can be precisely calculated and managed.