Cube – Definition With Examples

Welcome, young mathematicians, to another exciting exploration brought to you by Brighterly. As we embark on this journey of numbers and shapes, our subject for today is the fundamental and fascinating geometrical shape – the cube. Close your eyes and picture a perfect box, with all sides the same size. Think of dice or your favorite Minecraft character – what shape do you see? Yes, that’s a cube! But what really makes a cube, a cube? A cube is a three-dimensional geometric figure with all its sides equal in length, and every corner forms a perfect right angle. Think of it as a confident square that dared to step into the third dimension!

What is a Cube?

When you think of a box, or a dice, or even that building block you loved playing with as a kid, what shape comes to mind? That’s right! It’s a cube. A cube is a three-dimensional geometric shape that has all its sides equal in length, and every angle is a right angle. In mathematics, it’s considered a special kind of rectangular prism or square prism. Sounds like a mouthful, doesn’t it? But it’s not as complicated as it sounds. Think of a cube as a square that decided to become 3D and you’re on the right track!

Cube Definition in Maths

In mathematical terms, a cube is a three-dimensional solid object bounded by six square faces, facets, or sides, with three meeting at each vertex. This means that a cube has six equal square faces, twelve equal edges, and eight vertices. This is part of what we call Euclidean Geometry, the study of plane and solid figures on the basis of axioms and theorems employed by the Greek mathematician Euclid.

Properties of Cube

When it comes to understanding a cube, there are some important properties we need to look at. The properties of a cube can be broken down into three main aspects: its faces, edges, and vertices.

  1. Faces: A cube has six faces, each of which is a square of equal size. These faces meet at right angles, meaning each corner of a cube is a 90-degree angle.
  2. Edges: The edges of a cube are the lines along which two faces meet. A cube has 12 edges, all equal in length.
  3. Vertices: The vertices (or corners) of a cube are the points where the edges meet. A cube has eight vertices.

Cube Net

A cube net is a pattern that you can cut out and fold to make a model of a cube. It is a 2D representation of the 3D cube. Picture a cube that has been opened up at the edges and laid flat. That’s what a cube net looks like. It has six squares connected together in such a way that they can be folded to form a cube. The net of a cube consists of six squares connected in a specific way. There are actually 11 different ways (or nets) to fold a square to make a cube!

Cube Formulas

We use certain formulas to calculate the various aspects of a cube. These are the cube formulas:

  1. Volume of a Cube: V = a³ (where ‘a’ is the length of the edge)
  2. Surface Area of a Cube: A = 6a² (where ‘a’ is the length of the edge)
  3. Diagonal of a Cube: d = √3 * a (where ‘a’ is the length of the edge)

Surface Area of a Cube

The surface area of a cube is the total area that the surface of the cube covers. Imagine you wanted to paint a cube – the surface area is the amount of paint you would need to cover it completely. The surface area of a cube is calculated by taking the area of one of the faces (or sides) and multiplying it by six, because a cube has six equal faces. This is why the formula is A = 6a².

Lateral Surface Area of a Cube

Now, if we talk about the lateral surface area of a cube, it’s a bit different. The lateral surface area of a cube refers to the area of the four sides of a cube. It does not include the area of the top and bottom faces. Hence, the formula for lateral surface area is A = 4a².

Total Surface Area of a Cube

The total surface area of a cube includes all of its faces, meaning the top, bottom, and all the sides. Since all faces of a cube are square and equal in size, the total surface area of a cube can be found by multiplying the area of one face by six. Thus, the formula for the total surface area of a cube is the same as that for surface area, A = 6a².

Volume of a Cube

The volume of a shape measures the three-dimensional space that it occupies. For a cube, calculating the volume is quite easy. You simply need to cube the length of one of the sides (that is, multiply the length by itself twice). So, the formula for the volume of a cube is V = a³.

Diagonal of a Cube

A cube has four diagonals in three-dimensional space. These diagonals go from one corner of the cube, through the center, to the opposite corner. The formula to calculate the length of a diagonal in a cube is d = √3 * a.

Cube Shape

The shape of a cube is incredibly regular, with all angles and sides equal. Because of its uniformity, it’s used in various areas like architecture, design, gaming, and more. You can see the cube shape in everyday items like dice, Rubik’s cubes, and ice cubes.

How to Make a Cube Shape?

Making a cube shape can be a fun and educational activity. It can be as simple as folding a piece of paper. To make a paper cube, you’ll need a cube net. Simply print it out, cut along the edges, fold along the lines, and tape or glue the flaps together to create your cube.

Difference Between Square and Cube

One major difference between a square and a cube is the number of dimensions they have. A square is a two-dimensional shape with four equal sides and four right angles, while a cube is a three-dimensional object with six square faces, twelve equal edges, and eight vertices. In mathematical terms, if ‘a’ is the length of the edge of a square, its area is whereas the volume of a cube is .

Practice Questions on Cube

To solidify your understanding of cubes, here are some practice questions for you:

  1. If the length of the edge of a cube is 4 cm, what is its surface area?
  2. What is the volume of a cube with an edge length of 3 cm?
  3. If the diagonal of a cube measures 5√3 cm, what is the length of the sides?

Conclusion

So, here we are at the end of our mathematical adventure today. We dove into the world of geometry and explored one of its most simple, yet vital players – the cube. Together, with Brighterly, we discovered its core properties, the magic of cube nets, the important formulas, and the exciting differences between cubes and squares.

Like every great explorer, the knowledge we’ve gained during this journey is a stepping stone to new adventures. We hope that you will now look at cubes in a different light, seeing not just a shape but a collection of fascinating properties and possibilities. Remember, dear young mathematicians, the world is an oyster for those who are ready to explore and learn. So, don’t stop here; take your newfound understanding of cubes and let it be the foundation for your next exploration into the vast, wonderful world of mathematics!

Frequently Asked Questions on Cube

Let’s end our journey by addressing some frequently asked questions about cubes:

Is every square a cube?

No, every square is not a cube. While it’s true that both a square and a cube have all sides of equal length, it’s important to remember that a square exists in two dimensions (length and width), while a cube extends into three dimensions (length, width, and height). So, while every face (or side) of a cube is a square, the cube itself is a three-dimensional figure, whereas a square is a two-dimensional shape.

Can a cube have rounded corners?

In strict mathematical terms, a cube cannot have rounded corners. By definition, a cube is a three-dimensional object bounded by six square faces, with three meeting at each vertex at right angles. So, if a shape has rounded corners, it would not meet these criteria and therefore would not be classified as a cube.

How many edges does a cube have?

A cube has 12 edges. Remember, an edge is where two faces of the cube meet. Since a cube has six faces, and each face connects to four others, that results in twelve edges.

What is the surface area of a cube?

The surface area of a cube is the total area that the surface of the cube covers. It’s like the amount of paint you would need to cover all the outer faces of the cube without any gaps. You can calculate it by using the formula A = 6a², where a represents the length of an edge of the cube.

How to calculate the volume of a cube?

The volume of a cube represents how much space the cube takes up in three dimensions. It’s like how much water the cube could hold if it was hollow and you filled it up. To find the volume, use the formula V = a³, where a is the length of an edge. That means you multiply the length of the edge by itself twice to get the volume.

Information Sources:
  1. National Council of Teachers of Mathematics
  2. University of Cambridge – Cube
  3. Wolfram MathWorld – Cube

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