# Volume of prisms

## In a nutshell

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

## Prisms

### Definition

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.*

##### Examples

| | |

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. |

## Formulae for volumes of 3D shapes

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. | |

##### Example

*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 *$\underline{90cm^3}$.