Cube Formula

Cube Formula

A cube is a solid, three-dimensional object with six square faces. It is a geometric shape with six equal faces, eight vertices, and twelve equal edges. Cube Formula determines a cube’s surface area, diagonals, and volume. Students can learn all the formulas of cube and how to calculate volume, surface area and diagonal using Cube formula in this post by Extramarks.

What is a Cube?

A cube is a solid, three-dimensional object having six square faces and equal-length sides. Examples of cubes in real life include Rubik’s cubes, dice, and ice cubes, among others.

Properties of Cube 

 The following are the important properties of cube: 

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

What is Cube Formula

The Cube Formula are mentioned below:  

Cube Surface Area Formula

Cube Surface area is of two types Lateral Surface Area and Total Surface Area. The formulas for them are mentioned below:

Lateral Surface Area of Cube = 4a²

Total Surface Area = LSA + Area of the Top and Bottom Faces  

TSA = 4a² + a² + a²

TSA = 6a² 

Total Surface Area is also called Surface Area of Cube. Here, in the above formulas, a is side length of cube.

Cube Volume Formula

Cube volume formula is given as

Cube volume = a³ cubic units

Cube Diagonal Formula

  • The face diagonal formula of Cube is given as √2×Side
  • The body diagonal formula of cube is given as √3×Side

Examples Using Cube Formula

Example 1:  

Determine the cube’s surface area and volume if the side length is 10 cm. 

Solution:  If side a = 10 cm, then 

Consequently, using the cube’s surface area and volume equations, we may write; 

Surface Area = 6a² = 6×10² = 6×100, which is 600 cm². 

Volume of Cube = a³ = 10³ = 1000 cm³ is the volume. 

Example 2: 

Find the cube’s side length. Its volume is 512 cm³. 

Solution:  Given, Cube’s volume, V = 512 cm³. 

We are aware that a3 cubic units is the formula for a cube’s volume. 

512 thus equals a³

You can represent 512 as 8³. 

8³ = a³  

Consequently, a= 8 

As a result, the cube’s side length is 8 cm.

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FAQs (Frequently Asked Questions)

Cube is a three dimensional geometrical figure whose all sides are of same length

All of a cube’s faces are square, making it a three-dimensional version of the square. The faces of a cuboid, on the other hand, are all rectangles in three dimensions. 

The formula to get a cube’s surface area is 6a² square units, where “a” stands for the cube’s side length. 

The volume of a cube is calculated as a³ cubic units, where “a” is the side length, because every side of a cube is equal.