Unit Conversions for Volume

[Single speaker]

[on screen text, “Unit Conversions for Volume”]

Instructor: Hi. Welcome to the video on unit conversions for volume. [text fades, and a cube is shown on screen] First of all, let’s talk about the relationship between centimeters and liters. If I have a line that is 10 centimeters long, and then I square that by making a square that is 10 centimeters by 10 centimeters--pretend these sides are straight, so 10 centimeters by 10 centimeters-- [the instructor draws a square, labeling each side as “10 cm”] I now have an area that is 100 centimeters square because 10 centimeters times 10 centimeters equals 100 centimeters squared. Let’s write that down. 10 centimeters times 10 centimeters equals the 100 centimeters squared, meaning there are 100 little 1 by 1 centimeter squares in this entire big square. [writes “10cm x 10cm = 100 cm2”, then draws a small square in the corner of the bigger square] Here’s a cube with width 10 centimeters by 10 centimeters and 10 centimeters high. [labels each of the dimensions of the cube as “10 cm”] If we look at just 1 centimeter of depth on this cube, [a grid appears on one side of the cube, showing 100 small squares] it is comprised of 100 little cubes that are 1 centimeter by 1 centimeter by 1 centimeter. The entire large cube is made up of 10 layers, each containing 100 unit cubes. [the cube is filled by more layers of grids] 10 layers of 100 unit cubes is 1,000 unit cubes or centimeters cubed. [writes “1000 cm3” above the cube] 10 centimeters times 10 centimeters times 10 centimeters is equal to 1,000 centimeters cubed. [writes “10cm x 10cm x 10cm = 1000cm3”] 10 times 10 times 10 is 1,000, and centimeters times centimeters times centimeters is centimeters cubed. So a cube that is 10 centimeters by 10 centimeters by 10 centimeters is 1,000 cubic centimeters. This is defined as a liter--1 liter. [writes “1000cm3 = 1 Liter”] Similarly, each one of these 1 centimeter by 1 centimeter by 1 centimeter cubes, or in other words 1 centimeter cubed is equal to 1 milliliter. [writes “1cm3 = 1 ml”] So 1 milliliter is literally 1/1000 of a liter. So just 1 of these is 1 milliliter, and 1,000 milliliters makes 1 liter. So the unit conversion between centimeters cubed and liters in the metric system is very obvious.

[the screen changes, showing unit conversions from 1 yard to feet to inches with various colored lines]

Instructor: In imperial units, cubic inches, cubic feet, and cubic yards are calculated similarly based on their lengths cubed. For instance, let’s say we have a line that is 1-yard long. [the units disappear, and the instructor draws a line] This is equal to 3 feet. [writes “1 yd = 3 ft”]  If we make it a square yard, it’s now 1 yard by 1 yard or 3 feet by 3 feet. [draws a square, labeling each side as “1 yd” or “3 ft”] Let’s divide it into unit squares. [the instructor divided the square into 9 parts] Now each one of these is 1 foot by 1 foot for a total of  9 square feet--9 feet square, or square feet. [writes “9 ft2” above the square] So there are 9 square feet in 1 square yard. We can then do the same thing as we did with the metric units and now make it a square cube. [A grid appears, divided into 9 equal 1 foot cubes] Here is one square cube--1 by 1 by 1--which right here. And this represents 3 feet by 3 feet by 1 foot deep. We can make this a cubic yard by adding 2 more layers of unit cubes to the entire thing. [two more layers of the grid appear, forming a cube made of grids] So now we have 1 yard or 3 feet by 1 yard which equals 3 feet by 1 yard high or 3 feet high. [labels each side of the cube as “1 yd” and “3 ft”] So this is 1 cubic yard--1 yard cubed. But 1 yard cubed is equal to--each layer is made up of 9 units cubes--1, 2, 3, 4, 5, 6, 7, 8 , 9--and there are 3 layers for a total of 27 cubic feet because 3 feet times 3 feet times 3 feet is 27 cubic feet. [writes “1 yd3 = 27 ft3”] 

[the screen fades to a new page. There are all the names of the imperial units for volume, “Teaspoon”, “Cup”, “Tablespoon”, “Pint”, “Ounce”, “Quart”, and “Gallon”]

Instructor: Some of the other imperial units for volume are not quite as straightforward, particularly the units used in cooking or for liquids. If you ever need to do a unit conversion with some of these units, you can find the unit conversions in a book or on the internet. Some common conversions are that 3 teaspoons equal a tablespoon. 2 tablespoons equal an ounce. 8 ounces equal a cup. 2 cups equal a pint. 2 pints equal a quart, and 4 quarts equal a gallon. 1 quart is approximately 0.946 liters. So a quart is very close to 1 liter. Again, if you ever need to find unit conversions, there are lots of resources online to help you go from one unit to another.

[End of video]