A shape’s volume is a measure of its total 3-dimensional space. You can use the following simple formulas to help you calculate the volume of shapes like cuboids and prisms.
We've learned that the volume of a cuboid is its length multiplied by its width multiplied by its height (\(l \times w \times h\)).
The area of the green shaded end of the cuboid (the cross section) is \(w \times h\), so you can also say that the volume of a cuboid is: \(Volume = area~of~cross~section \times length\)
This formula works for all prisms:
a) What is the volume of this triangular prism?
b) What is the volume of this prism?
a) \(volume = area~of~triangle \times length\)
\[=(\frac{1}{2}\times{2~cm}\times{5~cm})\times{4~cm}\]
\[= \text{20 cm}^3\]
b) The area of the cross section is \(\text{5 cm}^2\) and the length is \(\text{8 cm}\), so the volume is \({5~cm}^{2}\times{8~cm}={40~cm}^{3}\).
Remember that the volume is:
\[the~area~of~the~cross~section\times the~length\]