A cube is a symmetrical three-dimensional shape made up of six equal squares. It is one of the simplest 3D shapes in mathematics due to its symmetry. Something that resembles a cube is often referred to as being “cubic.”

Pupils may wonder what the difference between a cube and a square is. There isn’t, as they share the symmetrical trait. However, a cube is a 3D object, whereas a square is a 2D object. Therefore, it’s best to describe a cube as being made up of squares rather than the same thing.

The next step up from this is a tesseract known as a 4D object. Much like a cube comprises six squares, a tesseract consists of eight cubes. This is a handy way of explaining to pupils that each new dimension builds on what came before.

As we’ve established already, a cube is a 3-D solid object with six square faces, and all the sides of a cube are of the same length. However, there are more unique properties that define what a cube is, which your pupils will have to know. To correctly identify a cube:

  • It must have six faces, 12 edges, and eight vertices.
  • It must have faces shaped like a square, making the breadth, height, and length the same.
  • The angles between any two faces or surfaces must be 90°.
  • The opposite planes, looks, and edges are parallel to each other.
  • Each vertex in a cube meets the three faces and edges.

How to calculate the surface area of a cube

When it comes to the calculations we do with 2D shapes; we only ever work out what their area is. However, with an extra dimension comes extra calculations as 3D shapes have a surface area and volume we have to figure out.

We’ll start with how to calculate the surface area of a cube. This is a bit simpler as the process isn’t as complicated because a cube is symmetrical. The formula we need to remember when we want to calculate the surface area of a cube = six × area of one square.

As your class will remember, to work out the area of a square, we have to multiply the length of one side by two. So let’s work with this example:

What is the surface area of a cube with 4cm sides?

So first things first, we must figure out the area of one square. As we know, the sides of the square are 4cm, and we need to multiply by two to find out the area of a square; we can do the following:

4cm x 2 = 8

Next, we must put our answer into our surface area formula. This leads to the following:

8cm * 6 = 48cm²

How to calculate the volume of a cube

To calculate the volume of a cube, we must know the following formula:

Volume of cube = Length ³

Let’s use the example of a cube with a side of 3cm. Thankfully, figuring out the volume is simple as the length is whatever the side is. So with our example, all we have to do is:

Volume = 3 x 3 x 3 = 27cm²

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