How Do Unit Cubes Help You Understand Volume in Maths?
Have you ever played the ludo? Yes! That is great. Then surely you have used dice. Isn't it? Can you tell the shape of a dice? Or, you might try to fix the Rubik’s Cube. What is the shape of a Rubik’s cube? The shape of both the objects is a ‘cube’. A cube is an object that has all edges equal in size. Can you count the number of edges a cube has? Yes, you are right, it is 12.
But the question is what is a unit cube? Let's read the complete article and get the answers to such questions.
What Is the Unit Cube?
Like any other cube, a unit cube is a three-dimensional object. It also has 12 edges. And, the major point to be focussed on is that the length of all edges is equal to 1 unit. A unit cube is also called a ‘Cube of Side 1’. It has six faces which are unit squares.
Unit Cube
The Volume of a Unit Cube
We know that the volume of a cube is calculated as:
Volume = side x side x side = (side)3
To evaluate the volume of a unit cube, we know that the side of a cube is 1 unit. Therefore,
Volume of unit cube = 1 x 1 x 1 = 13= 1
∴ The volume of unit cube = 1 unit3 or 1 cubic unit.
So, the volume of a cube is 1 cubic unit.
Now, let us calculate the surface area of a unit cube.
Surface Area of Unit Cube
A unit cube has 6 faces, and the dimension of each side is 1 unit. All the faces are square in shape.
So, the area of each face = Side x Side
= 1 unit x 1 unit
= 1 square unit
A unit cube has 6 faces of 1 square unit each.
Therefore, the total surface area of unit square = 6 x area of one face of a unit square
= 6 x 1 square unit
= 6 square units
Hence, the surface of the unit cube is 6 square units.
Do You Know?
A unit cube is used to calculate the density of any object. (How much mass an object has of one unit cube is known as the density of any object.)
It is also used to calculate the volume of other cubic or cuboidal objects. (We can calculate it by filling or building the object using the unit cube.)
Numerical Type Questions on Cubes
Question 1. What is the volume of an object that is made up of combining the six unit cubes?
Solution: The new shape is made by combining the six unit cubes.
We know that the volume of a unit cube is 1 cubic unit.
Therefore, the volume of the new object = 6 x 1 cubic unit
= 6 cubic unit
Question 2: What is the density of an object of mass 500 kg which occupies a space of a unit cube?
Solution: We know that the density of an object is equal to the mass of an object occupied by one unit cube.
So, density = $\frac{Mass}{Volume}$
Density = $\frac{500kg}{1 cubic unit}$
Density = 500 kg unit-3
A Tip for Parents
We request all parents to introduce their children to geometrical shapes. Show them daily-life examples of different shapes and their applications. Introducing different shapes not only helps them to learn the concept deeply but also opens further dimensions to increase their quantitative and numerical ability.
Conclusion
In this article, we have learnt about the cube and unit cube. We have also derived the value of the volume and surface area of a unit cube.
To know more about geometrical shapes and key terms, you can visit our website.
FAQs on What Is a Unit Cube? Definition, Facts & Simple Examples
1. What is a cube in simple terms for kids?
A cube is a special 3D (three-dimensional) shape that looks like a box with all sides being equal. Think of a dice or a Rubik's Cube. Every face of a cube is a perfect square, and all its edges (the lines where the faces meet) are the same length.
2. What are the main parts of a cube?
Every cube has three main parts that you can count:
Faces: These are the flat square surfaces. A cube has 6 faces.
Edges: These are the straight lines where two faces meet. A cube has 12 edges.
Vertices: These are the corners where the edges meet. A cube has 8 vertices (singular: vertex).
3. What is a unit cube?
A unit cube is the simplest type of cube used for measurement. It is a cube where the length of every side is exactly 1 unit. Because its sides are 1 unit long, its volume is exactly 1 cubic unit. It's like the basic building block for measuring the space inside larger shapes.
4. How is a cube different from a square?
The main difference between a cube and a square is their dimension. A square is a flat, 2D (two-dimensional) shape with four equal sides. You can draw it on paper. A cube is a solid, 3D (three-dimensional) object that has height, width, and depth. A cube is made up of six square faces.
5. Why is a unit cube important for measuring volume?
A unit cube is important because it gives us a standard way to measure volume. Volume is the amount of space an object takes up. To find the volume of a larger box-like shape, we can imagine filling it with unit cubes and counting how many fit inside. This count gives us the shape's volume in 'cubic units'.
6. What is the difference between a cube and a cuboid?
A cube is a special type of cuboid. The key difference is in their faces and edges:
A cube has 6 identical square faces and all its 12 edges are of equal length.
A cuboid also has 6 faces, but they can be rectangles and its length, width, and height can be different. A shoebox or a brick are examples of cuboids.
So, every cube is a cuboid, but not every cuboid is a cube.
7. How many unit cubes are needed to build a larger cube with side lengths of 2 units?
To build a larger cube with sides of 2 units, you would need 8 unit cubes. You can think of it as two layers. The bottom layer would be a 2x2 square made of 4 unit cubes. The top layer would be another 2x2 square of 4 unit cubes placed on top. This gives you a total of 4 + 4 = 8 cubes, creating a larger 2x2x2 cube.
8. What are some real-life examples of a cube?
You can find examples of cubes all around you! Some common ones include:
A standard dice used in board games.
A Rubik's Cube puzzle.
Ice cubes made in a square tray.
Sugar cubes.
Some types of gift boxes or building blocks.
