I show how we can indeed calculate the VOLUME of right rectangular prisms with fractional edge lengths by multiplying the three dimensions length, width, and height.
For example, we look at the unit cube (with dimensions 1 cm, 1 cm, and 1 cm), and pack it with little cubes with edge length 1/2 cm. That takes 8 cubes, therefore the volume of each those little cubes is 1/8 of a cubic centimeter. And, you do get the same result if you simply multiply the length, width, and height of the little cube: 1/2 cm × 1/2 cm × 1/2 cm = 1/8 cubic cm.
I show another similar example when the edge or side lengths are 1 1/2 in, 1 1/2 in, and 1 in.
Lastly we look at another unit cube, this time packed with little cubes with edge lengths of 1/3 unit. Similar reasoning as above shows us that the volume of each little cube is 1/27 of a cubic unit (since 27 little cubes make up the unit cube). And that is the same as 1/3 × 1/3 × 1/3.
This lesson is meant for 6th grade, and it specifically matches the common core standard 6.G.2 : "Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism."
In this 2nd video, we first review briefly the two formulas for the volume of a rectangular prism, and then delve into a realworld problem involving a room with a floor area of 9 1/2 feet by 12 feet, and height of 8 1/2 feet.
To find its volume, I first calculate the area of the floor, and then multiply that by the height.
Then, the question continues: if the ceiling is dropped so the room is only 8 ft high, how much volume does the room lose?
Area of parallelograms and triangles
Math Mammoth Geometry 2 — a selfteaching worktext with explanations & exercises (grades 67)
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