~ 7.12 ~

Learning Targets

• I can explain why the volume of a prism can be found by multiplying the area of the base and the height of the prism.

Any cross section of a prism that is parallel to the base will be identical to the base. This means we can slice prisms up to help find their volume. The volume of a three-dimensional figure is a measure of the amount of space that it occupies. Volume is measured in cubic units. For example, if we have a rectangular prism that is 3 units tall and has a base that is 4 units by 5 units, we can think of this as 3 layers, where each layer has 4 • 5 cubic units.

That means the volume of the original rectangular prism is 3(4 • 5) cubic units.

This works with any prism! If we have a prism with height 3 cm that has a base of area 20 cm², then the volume is 3 • 20 cm³ regardless of the shape of the base. In general, the volume of a prism with height h and area B is

V = B • h

For example, these two prisms both have a volume of 100 cm³.

cross section

A cross section is the new face you see when you slice through a three-dimensional figure.

For example, if you slice a rectangular pyramid parallel to the base, you get a smaller rectangle as the cross section.

This applet has 64 snap cubes, all sitting in the same spot on the screen, like a hidden stack of blocks. You will always know where the stack is because it sits on a gray square. You can keep dragging blocks out of the pile by their red points until you have enough to build what you want.

Click on the red points to change from left/right movement to up/down movement.