Volume of rectangular pyramids using cubes
About this video
The video finds the volume of a cube with side 5 (5 × 5 × 5 = 125 cubic centimetres). It then shows the cube can be split into three congruent pyramids, each with a square base matching a face of the cube and the same height, so each pyramid's volume is one third of the cube's.
You'll be able to
- find the volume of a cube by multiplying length, width and height.
- explain why one of three congruent pyramids that form a cube has one third of the cube's volume.
Key words
- cube
- A 3D shape with six square faces where all edges are the same length.
- volume
- The amount of space a 3D shape takes up, measured in cubic units.
- rectangular pyramid
- A 3D shape with a rectangle (or square) base and triangle sides meeting at a point.
- congruent
- Exactly the same shape and size.
Transcript
- [Speaker] We'll be exploring the volumes of rectangular pyramids today with cubes and rectangular prisms. This is a cube. All the sides are the same length. To find the volume of a cube, I can multiply the length by the width, by the height. For example, if the length of the cube is five and all sides are the same, then define the volume, I would do five times five times five equals 125 centimeters cubed.
I can break this prism into three rectangular pyramids that are all congruent. So now we have a cube that's actually made out of three rectangular pyramids, and we can see here that all of the rectangular pyramids are congruent. The base of each rectangular pyramid is a square.
The square is the same size as one face of our cube, and they all have the same height. Since all of these rectangular pyramids are congruent, they all have the same volume. To summarize so far, three congruent pyramids can form a cube, and the volume of one of the pyramids will be one third of the volume of the entire cube.
This is true for all cubes, but what about other rectangular prisms where the sides have different lengths?
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