Slices and area

We can see that the rectangular prism is made up of five copies of the 4 × 3 × 1 slice shown. The base area of the slices is 12 cm² and the height is 1 cm. We have five such slices in the original prism so we have:

\begin{align}V &= 5 × 12\\ &= 60\ \text{cm³}.\end{align}

Volume of a rectangular prism = Ah where A is the area of the base and h is the height.

Example 1

Find the volume of the rectangular prism pictured.

Solution

\begin{align}A &= 20 × 2\\ &= 40\ \text{cm²}\\ h &= 2\ \text{cm}\\ V &= Ah\\ &= 40 × 2\\ &= 80\ \text{cm³}.\end{align}

Note that volume is a cubic measure, common units being cm³, millilitres (mL) and litres (L).

\begin{align}1\ \text{L}\ &= 1000\ \text{cm³}\\ 1\ \text{mL} &= \dfrac{1}{1000}\ \text{L}\\ \text{so}\ 1\ \text{mL} &= 1\ \text{cm³}.\end{align}