A cube is a 3-dimensional solid object bounded by six square faces, facets, or sides, with three meetings at each vertex. It has 6 faces, 12 edges, and 8 vertices. In other words, we can also say that a cube is a block with the same length, breadth, and height.
A cube is a special case of the square prism. It is also known as a square parallelepiped, an equilateral cuboid, and a right rhombohedron
Some real-life examples of a cube are;
● Rubik’s Cube
● An Ice cube
Generally, we use the height, length, and breadth of a rectangular prism or cuboid to find out its volume and area but since the length, breadth, and height of a cube are the same so we can take advantage while calculating its volume or surface area.
The amount of space occupied by a three-dimensional solid is known as volume.
For eg. We have a cubical container and we want to store apple juice in it, so the measure of juice in liters that could be stored in the container is the volume or capacity of the given container.
The volume of a Cube
The volume of a rectangular prism is given by
V=Length * Breadth * Height.
But in the case of a cube, Length=Breadth=Height
Therefore, Volume of Cube= Length*Length*Length
Or Volume of Cube=Breadth*Breadth*Breadth
Or Volume of Cube=Height*Height*Height
So, we can generalize the formula for the Volume of Cube,
I.e. Volume =
Where a is the edge of the cube.
For example, we have a cubical block whose edge=4 inches. We have to find out the volume of the cubical block.
=> a= 4 inches, Volume = 4*4*4
Volume = (4)3
Volume = 64 cubic inches.
Surface area is the sum of the areas of all the faces of the 3 dimensional solid. It is the measure of the total area that the surface of the object occupies.
Surface Area of a Cube:
To find the surface area of a solid we calculate the sum of the area of all the faces of the solid, since we are talking about the surface area of a cube then we know that the area of all the faces will be the same.
There are 6 faces in a cube, therefore, the surface area of a cube will be,
Surface Area = 6a2
For example, we have a cubical box of 5 inches, therefore, the surface area of the cubical box will be,
Surface area = 6*52
Surface area = 6*25
Surface area = 150 square inches.
Properties of a cube
● All the faces of a cube are square
● All the faces or sides have equal dimensions.
● The angles in a cube are all right angles
● The edges opposite to each other are parallel.
Just like Cube, there are more # dimensional shapes
● Hexagonal Prism
● Pentagonal Prism
Tired of doing homework?
Well we do have a plan for you, have you ever thought of getting online homework help?
TutorBin can help you with your homework, you can get geometry help with just a tap. Our expert tutors can help you whenever you need them in the best way possible.
You can get your Math homework help from TutorBin as well as you can also take online sessions if you need to understand some concept. Our tutors are well-qualified individuals from topmost universities around the world, who can guide you, motivate you and help you with whatever doubts you have.
Frequently Asked Questions
- What is a cube?
A cube is a 3 dimensional solid, with 6 square-shaped faces, 12 edges, and 8 vertices. The height, length, and breadth of a cube are equal i.e. all 12 edges of the cube are equal.
2. How can you differentiate between a cube and a cuboid?
A cube is a 3-dimensional form of a square whereas a cuboid is the 3-dimensional form of a rectangle and it is also known as a rectangular prism.
3. Can you give an example of a cube?
There are many real-life examples of a cube, such as:
● Rubik’s Cube
● Ice cube
4. What is the formula to find out the volume of a cube?
The volume of a cube = a3
5. What is the formula to find out the surface area of a cube?
Surface Area = 6a2
6. What are some 3 dimensional shapes other than cube and cuboid?
There are many 3 dimensional shapes;
● Pyramids, etc.