Surface Area of a Cube Formula | Diagonal of a Cube & Volume of a Cube

What is Cube?

A cube is a three-dimensional figure with six square faces. When it is moving through space then it will become thicker. All cubes have six sides, one is the top, one is the bottom, and rest four sides make a square together. To count the sides of the cube, you have to look at the image carefully because two sides are hidden.

Further, the cube has eight corners and each corner is aligned at the right-angle. The top and bottom planes are parallel in nature and so the opposite sides too. The top and bottom sides are the perpendicular to other four sides too. In mathematics, a cube is a three-dimensional figure but it can be shown on the 2-dimensional surface too with the help of following properties –
Cube

All faces meet other four faces they form squares. All the plane angles are right angles and vertices meet 3 faces. The opposite edges on the cube are parallel to each other.

Surface Area of a Cube Formula

The surface area of a cube is the total space occupied outside the surface of the cube. It is generally measured in terms of square units. Hence, the other name for the cube is hexahedron because of six identical square faces. Each face has four edges and it makes a total of 12 edges in the cube. The Surface area of a cube formula is given as –

\[\large Surface\;area\;of\;Cube=6a^{2}\]
Where,
a is the side length of the cube.
Question 1: What is the surface area of a cube of side 5 cm ?
Solution:
Given,
Side of the cube = a = 5 cm
Surface Area of a Cube
= 6a2
= 6 x 52 cm2
= 6 x 25 cm2
= 150 cm2

Diagonal of a Cube Formula

The diagonal of a cube is the measurement that cuts through the center of a cube. The diagonal of the face would not be the major diagonal but it can be computed by multiplying one side of the cube with the square root of three. In Mathematics, the diagonal of a Cube formula is given as –

\[\LARGE Diagonal\;of\;a\;Cube=\sqrt{3}a\]
Where,
a is the side length of the cube.

The Volume of a Cube Formula

The Cube has all edges of the same length and is measured in cubic units. The volume of a cube is found by multiplying the number with itself three times. For instance, if the length of an edge is 5, the volume is 53

The cube is a 3D structure whose length is measured in cubic units. To find the volume of a cube, you need to multiply the sides of a cube three time. For example, if you wanted to calculate the volume of a cube with length 5 then it is written as 53= 5 × 5 × 5 = 125. In mathematics, the volume of a cube formula is given as –

\[\large Volume\;of\;a\;cube=a^{3}\]
Where,
a is the side length of the cube.

Where a is the length of the cube and it may also be written as – a*a*a

The applications of cubes are common in daily mathematics like to compute power or exponents. This is also easy to find the side of a cube if the surface area or volume is given. In this case, you just need to rearrange the formula to compute the length of the side of a cube. Further, cubes are also used in designing multiple things like containers, cardboard box, or wooden blocks for construction etc.


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