Cube: Meaning, Digits and Addition

Cubes are a three-dimensional solid figure having equal sides on all sides. Dice, which we use in ludo, are a common example of a cube.

• If we have a cube with a side length of 1 unit, and we calculate the number of such cubes needed to make another cube with side lengths of 2,3,4, or 5, we get values like 8,27,625 and so on.
• It's worth noting that the figures we got above can also be obtained by multiplying the lengths of the sides three times. For instance, 3 x 3 x 3 = 27 or 2 x 2 x 2 = 8 and so on.
• The perfect cubes, often known as cube numbers, are created by multiplying a natural number three times.

Key Takeaways: Cubes, Units, Digits, odd, even, negative, addition, cube number, cube root

Also read: Isosceles Triangle Theorems

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What are Cubes?

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The result of multiplying an integer by itself three times is known as its cube number. A cube number is a number formed by multiplying three identical numbers. The volume of a cube is the best example of a cube number in geometry.

A cube, as previously stated, is a three-dimensional object.

A solid form with six faces, in three-dimensional space, a cube is one of the most basic shapes. A cube's six faces are all squares, which is a two- dimensional shape.

A cube's form is sometimes referred to as "cubic". A cube can also be thought of as a block because its length, width, and height are all the same. It also contains 8 vertices and 12 edges, with three of the edges meeting at one vertex point. Examine the image below and identify the faces, edges, and vertices. It's also known as a right rhombohedron, an equilateral cuboid, and a square parallelepiped. The cube is one of the platonic solids, and it is a convex polyhedron with square faces on all sides. The cube is said to have octahedral or cubical symmetry. The square prism is a specific instance of the cube.

The result of multiplying an integer by the same integer three times is known as cube number. Perfect cubes are another name for cube numbers. For instance, 5 x 5 x 5 = 5³ = 125.

As a result, a cube number is a number with the exponential power of three, or a number multiplied by three times. Because a negative number multiplied by the same negative number three times produces a negative number, cube numbers of positive numbers are positive while cube numbers of negative numbers are negative. For instance (-7)³ = -7 x -7 x -7 = -343( three negative signs multiplied by each other, results in a negative sign). When we multiply -7 three times, we get -343 as a result, which is a negative cube number. Here are some cube number instances.

Here are some representations of the cube numbers.

• -8 x -8 x -8 = 8³ = -512
• 13 x 13 x 13 = 13³ = 2197
• -2 x -2 x -2 = 2³ = -8
• 45 x 45 x 45 = 45³ = 91125

A cube's volume is equal to its length, breadth, and height in geometry. Because it's a cube, the length, breadth, and height of the cube are all the same. As a result, the volume of the cube equals a³, where an equal length, height, and breadth. This indicates that the cube's volume is a cube number.

The video below explains this:

Cube Detailed Video Explanation:

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Cube Numbers Units Digits

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The cube number of a number is either odd or even, depending on whether the number is odd or even. The nature of the cube numbers unit digit determines this.

1. If an integer is odd, the unit digit of its cube numbers is also odd.
2. If an integer is even, the unit digit of its cube number is also even.

The unit digit of a number and the units digit of the cube of that number are shown in the table below:

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Addition of Consecutive Odd numbers

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1 = 1 = 1³

3 + 5 = 8 = 2³

7+ 9+ 11 = 27 = 3³

13+ 15 + 17 + 19 = 64 = 4³

21+ 23+ 25 + 27+ 29 = 125 = 5³

As we can see from the pattern above, if we need to get the x³, we will require x consecutive odd numbers whose sum equals x³.

For all-natural integers, this pattern is true. Also, if we need to discover x³, we should add x natural numbers in a row, starting with an odd natural number.

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Properties of Cube

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The following are some of the most important characteristics of a cube:

• It has a square form to all of its faces.
• All of the faces or sides are the same size.
• The cube's plane angles are all right angles.
• Each of the four faces common into contact with the others.
• The three faces and three edges are met by each of the vertices.
• The edges on opposite sides are parallel.

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Formula of Cube

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The cube's surface area and volume are addressed below:

Surface Area of a cube

We know that the area of any shape is defined as the plane region it occupies. Because a cube is a three-dimensional plane. We must compute the surface area of the cube covered by each face because a cube has six faces. The formula for calculating surface area is given below.

Assume that an is the cube's edge.

a² = Area of one face = Area of a square

The cube has six square faces, as we know.

Lateral surface area = 4a²

Total surface area = LSA + Area of the top and bottom faces

TSA = 4a² + a² + a²

TSA = 6a²

Volume of Cube

The volume of a cube is the amount of room it can hold. If an object is cubical and we need to immerse any material in it, such as water, the amount of water to be kept in the object in litres is computed by its volume. The volume formula is as follows:

• The volume of cube = a³ cubic units

Length of Diagonal of the cube

If a is the length of the side, then,

• Length of diagonal of the face of the cube = √2 a
• Length of diagonal of cube = √3 a

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How cube is different from a square?

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The most significant distinction between the square and the cube is that the square is a two- dimensional figure with only two dimensions: length and breadth, but the cube is three dimensions: length, breadth and height. The cube is made from a square shape.

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Points to Remember

The facts about cube numbers are presented below:

• The last digit of a number and the last digit of the number's cube number will remain the same, with the exception that 2 will become 8 and 8 will become 2 and 3 will become 7 and 7 will become 3.
• When you cube even numbers, you'll get an even number. For instance, 2³ = 8 and 4³= 64. When you cube odd numbers, you will get an odd number. For instance, 3³ = 27 and 5³ = 125.
• Integers can be positive or negative in perfect cube numbers. For example, the perfect cubes of 2 and -2 are 8 and -8, respectively.
• A sum of successive odd numbers can be used to express perfect cubes.

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