Video: Converting between Units of Volume

1 fluid ounce is equal to approximately 30 mL. A can of soda pop has a volume of 12 fl oz. What is the volume of a can of soda pop in cubic meters?

02:03

Video Transcript

One fluid ounce is equal to approximately 30 milliliters. A can of soda pop has a volume of 12 fluid ounces. What is the volume of a can of soda pop in cubic meters?

We want to solve for the volume, we’ll call it capital 𝑉, of a can of soda pop in cubic meters. We’re told that one fluid ounce is approximately 30 milliliters and that a can of soda pop has a volume of 12 fluid ounces. What we want to do then is take our volume of 12 fluid ounces and convert it to some number of cubic meters.

So, we begin with our initial given volume, 12 fluid ounces. We’re told that one fluid ounce was equal to 30 milliliters. So, if we multiply our given volume by that conversion factor, 30 milliliters per one fluid ounce, then we see, when we multiply these two numbers together, the units of fluid ounces cancels out. And we’re left with units of milliliters.

That’s a good start. But we want our final answer 𝑉 in terms of units of cubic meters. So, now we seek for the conversion factor between liters and cubic meters. We find that one liter is equal to 0.001 meters cubed. Or one milliliter is equal to one times 10 to the negative sixth cubic meters. When we multiply our fraction by this conversion ratio, we see that the units of milliliters appear in the numerator and denominator. So, as we multiply it through, they cancel out just like fluid ounces did.

We’re left with a result in units of cubic meters, which is what we were seeking for. To find the value, the actual volume, we only need now to multiply these three fractions together. When we do, we find a volume of 3.6 times 10 to the negative fourth cubic meters. That’s the volume of a can of soda pop expressed in cubic meters.

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