Cube Has How Many Faces

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

Cube

A cube can be visualized in the grade of a square prism. This is because the faces of a cube are in the course of a foursquare 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 peak are the aforementioned.
The angles betwixt any ii 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 whatsoever 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 exist 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 some other. A cube has 12 edges.

Faces of cube

The face up of any geometrical effigy is the individual apartment surfaces of a solid object. A cube has 6 faces.

Formula of cube

Surface Surface area of Cube = 6a² in foursquare 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 expanse of the cube if its side is 6 cm?

Solution:

Here we need to find the surface expanse of the cube.

Given:

Side of the cube = 6 cm

As nosotros know that

Surface surface area of the cube = 6 × side × side

Surface surface area of the cube = 6 × side^two

Surface area of the cube = 6 × half dozen²

Expanse of the cube = 216 cm^two

Therefore,

Surface surface area of the cube is 216 cm².

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

Solution:

Here we demand to detect the book of the cube

Given:

Side of the cube = 4 m²

As we know that

Book of the cube = Side × Side × Side

Volume of the cube = Side^three

Volume of the cube = 4^three

Volume of the cube = iv × four × 4

Volume of the cube = 64 g³

Therefore,

Book of the cube is 64 grand^three.

Question 3. Find how many pocket-sized cubes can be made from a big cube of side 16 thousand in small cubes of side iv m?

Solution:

Hither nosotros need to find out how many small cubes can be made out of i big cube.

As we know that

Volume of cube = Sideⁱⁱⁱ

Volume of large cube = Side × Side × Side

Book of big cube = 16 × 16 × 16

Volume of big cube = sixteen³

Volume of big cube = 4096 thousand³

Farther,

Book of small-scale cube = Side × Side × Side

Volume of minor cube = 4 × 4 × 4

Book of small-scale cube = 4³

Book of small cube = 64 m³

At present,

Number of small cubes that can be made from the big cubes = Volume of big cube/Book of small cube

Number of pocket-sized cubes = 4096/64

Number of pocket-size cubes = 64

Therefore,

64 pocket-size cubes volition be made out of the big cube.

Question 4. If the surface area of a cube is 486 m². So detect the volume of the cube?

Solution:

Here nosotros need to find the book of the cube from a given surface expanse

Given:

Surface area of the cube = 486 m^two

As we know that

Surface surface area of the cube = 6 × Side²

486 = half-dozen × Side^two

Side² = 486/6

Side^two = 81

Side = √81

Side = 9 one thousand

Now,

Volume of cube = Side³

Volume of cube = 9^three

Volume of cube = nine × ix × nine

Book of cube = 729 m³

Therefore,

Volume of the cube is 729 m³.