Volume of prisms

In a nutshell

The volumes of various 3D shapes can be calculated by using their respective formulae.

A prism is a 3D shape that is a 2D shape stretched in the third dimension. The 2D shape is called it's cross-section.


This is a prism with a cross-section that is a hexagon. Therefore, this shape is called a hexagonal prism.	This is a prism with a cross-section that is a triangle. Therefore, this shape is called a triangular prism.	A cylinder is also a type of prism, it has a circular cross-section.

Here are the 3D shapes that you need to be able to calculate the volumes of:

SHAPE	FORMULA	DIAGRAM
Cube	$V=x\times x\times x=x^3$ Where $x$ is the length of a single side.
Cuboid	$V=\text{length}\times\text{width}\times\text{height}$ $V=lwh$
Cylinder	$V=\pi \times \text{radius}^2\times \text{height}$ $V=\pi r^2 h$
Prism	$V=A\times l$ Where $A$ is the area of the cross-section, and $l$ is the length.

A prism has a cross-sectional area of $7.5cm^2$ and a length of $12cm$ . What is the volume of the prism?

Substitute $A=7.5$ and $l=12$ into the formula:

$\begin{aligned}V&=A\times l\\&=7.5\times12\\&=90\end{aligned}$

The volume of the prism is $\underline{90cm^3}$ .