DISCOVER

# Similarities & differences of cubes & cuboids

Both a cube and a cuboid are three-dimensional solid objects with six rectangular faces each. However, all the faces of a cube are square. The faces of both a cube and a cuboid are perpendicular to other faces they meet at an edge. In other words, they meet at 90 degrees. Cube-shaped and cuboid-shaped objects are commonplace, such as dice, wardrobes and books.

## Faces

Every cube and every cuboid has exactly the same number of faces, namely 6. The nets of every cube and every cuboid also have 6 faces. A cuboid can have square faces but a cube cannot have any faces that are not square. If you can see only a single face of a cube or cuboid, you cannot tell which it is if the face is a square. If you can see only a single face of a cube or cuboid, you can tell which it is if the face is a rectangle that is not a square.

## Corners

Every cube and every cuboid has exactly the same number of corners, namely 8. The corners are always in the same places in relation to the faces for both cubes and cuboids, a meeting point for three surfaces at 90 degrees to each other. If you can only see the corner of a cube or cuboid, you cannot tell which it is.

## Dimensions

The length, width and height of a cube are all the same. If you know the length, you also know the width and height. In a cuboid, this is not the case. Knowing the length does not mean you also know the width and height. You can make a cube from some cuboids with one cut. You can make a cuboid from any cube with one cut. In fact, you can make two cuboids from any cube with one cut.

## Volume

The volume of a cube is l³ where l is the length. In practical terms, for a cube you need to take only one measurement to be able to work out the volume, by cubing the figure. The volume of a cuboid is l x w x h, where l is the length, w is the width and h is the height, according to mathematics teachers Graham Newman and Ron Bull. In practical terms, for a cuboid you have to take three measurements to be able to work out the volume, by multiplying them together.