How many faces, edges, and vertices does a cube have?

Mensuration is a division of mathematics that deals with the study of various available geometrical figures and their associated parameters such as area, length, volume, lateral surface area, surface area, etc.

Cube

A cube can be visualized in the form of a square prism. This is because the faces of a cube are in the form of a square and are also platonic solid in nature. The faces of a cube are also known as planes.

Properties of a Cube

All the faces are square-shaped, which implies that the length, breadth, and height are the same.
The angles between any two faces or surfaces are equivalent to 90°.
The opposite planes are parallel to each other.
The opposite edges are parallel to each other.
Each of the faces forms intersection with four faces.
Each of the vertices intersects with three faces and three edges.

Vertices of cube

A vertex of any figure is a point where two or more line segments form an intersection. It can be considered as a corner. There are 8 vertices in a cube.

Edges of cube

An edge in any geometrical figure can be considered as a line segment where any two faces form an intersection. They form the skeleton of the 3D shapes. It forms a boundary joining one vertex (corner point) to another. A cube has 12 edges.

Faces of cube

The face of any geometrical figure is the individual flat surfaces of a solid object. A cube has 6 faces.

Formula of cube

Surface Area of Cube = 6a² in square units

Where, ‘a’ is the side of the cube

Volume of cube = a³ cubic units

Where, ‘a’ is the side of the cube

Sample Questions

Question 1. Find the surface area of the cube if its side is 6 cm?

Solution:

Here we need to find the surface area of the cube.
Given:
Side of the cube = 6 cm
As we know that
Surface area of the cube = 6 × side × side
Surface area of the cube = 6 × side²
Surface area of the cube = 6 × 6²
Surface area of the cube = 216 cm²
Therefore,
Surface area of the cube is 216 cm².

Question 2. Find the volume of the cube if its side is 4 m²?

Solution:

Here we need to find the volume of the cube
Given:
Side of the cube = 4 m²
As we know that
Volume of the cube = Side × Side × Side
Volume of the cube = Side³
Volume of the cube = 4³
Volume of the cube = 4 × 4 × 4
Volume of the cube = 64 m³
Therefore,
Volume of the cube is 64 m³.

Question 3. Find how many small cubes can be made from a big cube of side 16 m in small cubes of side 4 m?

Solution:

Here we need to find out how many small cubes can be made out of one big cube.
As we know that
Volume of cube = Side³
Volume of big cube = Side × Side × Side
Volume of big cube = 16 × 16 × 16
Volume of big cube = 16³
Volume of big cube = 4096 m³
Further,
Volume of small cube = Side × Side × Side
Volume of small cube = 4 × 4 × 4
Volume of small cube = 4³
Volume of small cube = 64 m³
Now,
Number of small cubes that can be made from the big cubes = Volume of big cube/Volume of small cube
Number of small cubes = 4096/64
Number of small cubes = 64
Therefore,
64 small cubes will be made out of the big cube.

Question 4. If the surface area of a cube is 486 m². Then find the volume of the cube?

Solution:

Here we need to find the volume of the cube from a given surface area
Given:
Surface area of the cube = 486 m²
As we know that
Surface area of the cube = 6 × Side²
486 = 6 × Side²
Side² = 486/6
Side² = 81
Side = √81
Side = 9 m
Now,
Volume of cube = Side³
Volume of cube = 9³
Volume of cube = 9 × 9 × 9
Volume of cube = 729 m³
Therefore,
Volume of the cube is 729 m³.

My Personal Notes

Last Updated : 28 Nov, 2021

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