Volume of Right Prisms

Student Summary

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. 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 454\boldcdot 5 cubic units. The volume of the figure is the number of cubic units that fill a three-dimensional region without any gaps or overlaps.

Two images. First, a prism made of cubes stacked 5 wide, 4 deep, 3 tall. Second, each of the layers of the prism is separated to show 3 prisms 5 wide, 4 deep, 1 tall.

That means the volume of the original rectangular prism is 3(45)3(4\boldcdot 5), or 60, cubic units.

This works with any prism! If we have a prism with a height of 3 cm that has a base with an area of 20 cm2, then the volume is 3203\boldcdot 20 cm3 regardless of the shape of the base. In general, the volume of a prism with height hh and area BB is

V=Bh\displaystyle V = B \boldcdot h

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

Prism with triangular base, area 20 centimeters squared, and height 5 centimeters.

Prism with irregular base, area 25 centimeters squared, and height 4 centimeters.

Visual / Anchor Chart

Standards

Addressing
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7.G.B.6

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