# Cuboids, Rectangular Prisms and Cubes

*Go to Surface Area or Volume.*

A **cuboid** is a box-shaped object.

It has six flat faces and all angles are right angles.

And all of its faces are rectangles.

It is also a prism because it has the same cross-section along a length. In fact it is a **rectangular prism**.

## Examples of Cuboids

Cuboids are very common in our world, from boxes to buildings we see them everywhere. We can even fit them inside other cuboids!

A building

A box with a

slot as a handle

Cuboids in a

cuboid room

Boxes for model trains

Now that's just silly!

## Square Prism

When at least two of the lengths are equal it can also be called a **square prism**.

(Note: we can still call it a rectangular prism if we want!)

## Cube

When all three lengths are equal it is called a **cube** (or hexahedron)

and each face is a square.

A cube is still a prism.

And a cube is one of the Platonic Solids.

So:

- A cube is just a special case of a square prism, and

- A square prism is just a special case of a rectangular prism, and

- They are all cuboids!

Note: The name "cuboid" comes from "cube"** **and * -oid* (which means "similar to, or resembling") and so says "it is

*like*a cube".

Another use of ** -oid** is when we talk about the Earth being a spheroid (not exactly a sphere, but close).

## Surface Area

The surface area is found using the formula:

Area = 2 × Width × Length + 2 × Length × Height + 2 × Width × Height

Which can be shortened to:

A = 2wl + 2lh + 2hw

### Example: Find the surface area of this cuboid

A | = | 2wl + 2lh + 2hw |

= | 2×4×10 + 2×10×5 + 2×5×4 | |

= | 80 + 100 + 40 | |

= | 220 |

## Volume

The volume of a cuboid is found using the formula:

Volume = Length × Width × Height

Which can be shortened to:

V = l × w × h

Or more simply:

V = lwh

### Example: Find the volume of this cuboid

V = lwh = 10×4×5 = 200 |