Here ‘a’ is length of cube, ‘a’ is height of cube and ‘a’ is width of cube, Suppose, we have a cube, whose length, height and width is equal to 5 inch, then– Volume of cube = a * a * a, = 5 * 5 * 5, = 125 inch ^{3}.Surface area of cube = 6 * a ^{2},= 6 * (5) ^{2},= 6 * 25, = 150 inch ^{2.}So, volume of cube is 125 inch ^{3} and Surface Area of Cube is 150 inch^{2}, where length, height and width are equals to 5 inch.All three sides length, width and height of cubes are define in 3 d geometry like here in above example length, width and height of cubes are 5 inch are define in 3 dimension and volume of given cube is 125 inch ^{3} and surface area of this 3d solid geometry, which is called as a cube is 150 inch^{2}. This is all about 3d cube geometry. |

Let us now see what is Surface Area Of Cube, it can be as combined area of all the faces of the cube or combined area of all 6 Square faces.

Area of one face of a cube is given by a

^{2}, where ‘a’ is the length of the face of cube, therefore The Surface Area Of A Cube can be calculated by adding area of all 6 faces of cube.

Area of one face is a

^{2}as we calculated earlier, so surface area of cube is given by:

**Surface area of cube = (a**

^{2 }+a^{2 }+ a^{2 }+ a^{2 }+ a^{2}+ a^{2}) = 6a^{2}.Therefore surface area of a cube equals to six multiplied by square of its side or 6 a

^{2}.

Suppose we have to calculate the surface area of a cube whose side length is equals to 18 inch.

First we will square the side we get,

a

^{2}= a * a = 18 * 18 = 324.

We know that Surface Area Cube is equals to 6a

^{2}, therefore we get,

Surface area of cube = 6a

^{2}= 6 * 18

^{2 }= 6 * 324 = 1944 inch

^{2}.

Therefore surface area of cube is equals to 1944 inch

^{2}

_{.}

Now calculate the surface area of a cube whose side length is equals to 2 inch.

First Square the side = a

^{2}= 2 * 2 = 4,

Now multiply a

^{2 }by 6a

^{2}, we get

6a

^{2}= 6 * 2 * 2 = 24 inch

^{2},

Therefore surface area of this cube is equals to 24 inch

^{2}.

This is how we calculate the surface area of cube.

In Geometry we study about the different figures, two dimensional and three dimensional. For three dimensional figures, we need to learn about the capacity (which we call the volume) and the surface areas of the different shapes. Here we will study about volume of Cube. A cube is the three dimensional figure, which we say has 6 faces, and each face of which is in the form of the Square. In daily life applications, we come across many situations, where we need to find the volume of the objects, which are in the shape of cube, to find the volume of such shapes, we need to simply know the length of one side of the cube, and the volume can be calculated. As we say that the cube is the three dimensional figure, which is formed by joining 6 faces of the square shape and all the six faces are of the same measure. If we talk about the example of the cubes, the dice, the sugar cube, ice cubes all are the examples of the cubes in our daily life.

To learn about the volume of the cube, we Mean to find the capacity of the figure which is in the form of the cube. In order to find the volume of cubes, we mean that how much space of the three dimensions does the figure occupy, and it is measured in unit cubes. Here to find the volume of the cube, we write the formula:

Volume of the cube = Product of the three sides of the cube

Here the measure of all the three sides are same, so we say that the volume of the cube as = side * side * side.

Or it can be written as volume of the cube = side

^{3}.