Lesson 4: Volumes of Rectangular Prisms

Property

The volume of a prism is the product of the height by the area of the base.
That is, if the area of the base is $B$ and the height is $h$, volume is $V = Bh$.

Examples

• A rectangular prism with a base of $5 \text{ cm} \times 6 \text{ cm}$ and a height of $12 \text{ cm}$ has a volume of $V = (5 \times 6) \times 12 = 360 \text{ cm}^3$.

• A triangular prism has a base area of $30 \text{ in}^2$ and a height of $7 \text{ in}$. Its volume is $V = 30 \times 7 = 210 \text{ in}^3$.

Property

Cube whose edge is of length $L$:

Volume $= L^3$

Property

When the volume and two dimensions of a rectangular prism are known, the missing dimension can be found by rearranging the volume formula: $V = lwh$.
Solve for the unknown dimension by dividing the volume by the product of the known dimensions.

Examples