- MPM1D, MFM1P - develop, through investigation (e.g., using concrete materials), the formulas for the volume of a pyramid, a cone, and a sphere (e.g., use three-dimensional figures to show that the volume of a pyramid [or cone] is 1/3 the volume of a prism [or cylinder] with the same base and height, and therefore that V
_{pyramid}= V_{prism}/3

- Each student or group needs six of the large nets to make their rectangular prism and three of the small nets to make the cube. See below to download the nets.
- Note that each of these shapes is a pyramid, just non symmetrical.

Note that these instructions are for students. You may just wish to do this as a demo.

- Have the students construct the nine shapes using the nets (6 large and 3 small).
- Taking the six large shapes, construct three symmetrical pyramids. Note the dimensions (size of base and height).
- Using the same six shapes, create a rectangular prism. Note the dimensions (size of base and height).
- How do the height and base of the prism compare to the one of the symmetrical pyramids?
- How do the volumes of each pyramid compare to that of the prism?
- Taking the three small shapes, note the type of solid and its dimensions (size of base and height)
- Using the same three shapes construct a cube. Note the dimensions (size of base and height)
- How do the height and base of the cube compare to each non symmetrical pyramid?
- How do the volumes of each non symmetrical pyramid compare to that of the cube?
- If you had
__any__prism and a pyramid with the same base and height, how would the volume of the pyramid compare to the prism?

- A rectangular prism in six parts (pdf) (doc) Answers (pdf) (doc)
- A cube in three parts (pdf) (doc) Answers (pdf) (doc)

Did you use this activity? Do you have a way to make it better? If so tell us in the comment section. Thanks

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