Volume

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.

Part of

Perimeter, Area, Volume

Volume of a prism

Volume of a cuboid diagram, with one end of the cuboid shaded in green

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: $Volume = area~of~cross~section \times length$

Different types of prism

This formula works for all prisms:

3 different types of prisms

$\text{volume~of~a~cylinder}=\text{area~of~circle}\times\text{length}$
$\text{volume~of~triangular~prism}=\text{area~of~triangle}\times\text{length}$
$\text{volume~of~L-shaped~prism}=\text{area~of~L-shape}\times\text{length}$

Question

a) What is the volume of this triangular prism?

Volume of a triangular prism

b) What is the volume of this prism?

Volume of a triangular 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:

$the~area~of~the~cross~section\times the~length$

Move on to Test