Sum of cube Formula with Example and PDF

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Sum of cube Formula with Example and PDF

 

Sum of cube Formula with Example

A Cube is a solid three-dimensional figure, which has 6 square faces, 8 vertices and 12 edges. It is also said to be a regular hexahedron. You must have seen 3 × 3 Rubik’s cube, which is the most common eg. in the real-life and it is helpful to enhance brainpower. In the same way, you will come across many real-life examples, such as 6 sided dices, etc. Solid geometry is all about three-dimensional shapes and figures, which have surface areas and volumes. The other solid shapes are cuboid, cylinder, cone, sphere. . We also, learn the surface area formula for the cube along with its volume formula.

What is cube?

As discussed earlier, a cube is a 3-D solid shape, which has 6 sides. A cube is one of the simplest shapes in the three-dimensional space. Sometimes, the shape cube is considered as “cubic”. We can also say that a cube is considered as a block, where all the length, breadth and height are the same. , It has 8 vertices and 12 edges such that 3 edges meet at one vertex point. Check the given image below, defining its faces, edges and vertices. It is also known as a square parallelepiped, an equilateral cuboid and a right rhombohedron. The cube is one of the platonic solids and it is considered as the convex polyhedron where all the faces are square. We can say that the cube has octahedral or cubical symmetry. A cube is the special case of the square prism.

Sum of cube Formula with Example and PDF
Sum of cube Formula with Example and PDF

Properties of Cube

The following are the important properties of cube:

  1. It has all its faces in a square shape.
  2. All the faces or sides have equal dimensions.
  3. The plane angles of the cube are the right angle.
  4. Each of the faces meets the other four faces.
  5. Each of the vertices meets the three faces and three edges.
  6. The edges opposite to each other are parallel.

Cube of any digit, forms by multiplying the digit by itself three times. For instance, to find the 43 we need to multiply  4 three times: 4 ×× 4 = 64

Note: we write down “4 cube” as 43  (the little 3 means the number appears three times during the multiplication process.

The Cube Formula for any value ‘x’ is given as,

x3=x×x×x

Cube of any digit, forms by multiplying the digit by itself three times. For instance, to find the 53 we need to multiply 5 three times: 4 ×× 4 = 125

Note: we write down “4 cube” as 43  (the little 3 means the number appears three times during the multiplication process.

The Cube Formula for any value ‘x’ is given as,

x3=x×x×x

Cube Examples

Example 1:

If the value of the side of the cube is 10 cm, then find its surface area and volume.

Solution:

Given, side, a = 10 cm

Therefore, by the surface area and volume formula of the cube, we can write;

Surface Area = 6a2 = 6 × 202 = 6 × 400.= 2400 cm2

Volume = a= 203 = 8000 cm3

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