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Converting Cubic Feet to Liters

Worked Unit Conversion Example Problem

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This example problem demonstrates how to convert cubic feet to liters.

Problem:

What is this volume of 1 cubic foot in liters?

Solution:

Many conversion factors are difficult to remember. Cubic feet to liters would fall into this category. The unit cancelling method is useful to perform this kind of conversion. It uses multiple easily remembered conversions to relate the original units to the final units.

1 foot = 12 inches
1 inch = 2.54 centimeters
1000 cubic centimeters = 1 liter

Using these steps we can express a feet to centimeters as:

distance in cm = (distance in ft) x (12 in/1 ft) x (2.54 cm/1 in)
distance in cm = (distance in ft) x 30.48 cm/ft


Now we need to convert these distances into volume measurements of cm3 and ft3.
Cube Volume = (linear measurement)3, so

volume in cm3 = [(distance in feet) x 30.48 cm/ft]3
volume in cm3 = (volume in ft3) x 28316.85 cm3/ft3

Now we can convert cubic centimeters to liters

volume in liters = (volume in cm3) x (1 L/1000 cm3)
volume in liters = (volume in cm3)/1000 L/cm3

Insert the cubic volume from the previous step: volume in liters = [(volume in ft3) x 28316.85 cm3/ft3)]/1000 L/cm3
volume in liters = (volume in ft3) x 28.317 L/ft3

Now we have our conversion factor of cubic feet to liters. Insert 1 cubic foot into the volume in ft3 part of the equation

volume in liters = (1 ft3) x 28.317 L/ft3
volume in liters = 28.317 L

Answer:

One cubic foot is equal to 28.317 liters of volume.

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