What Is Cube? Examples, Step by Step Illustration and More

The concept of cube plays a key role in mathematics and is widely applicable to both real-life situations and exam scenarios. From geometry to algebra, understanding cubes helps students grasp more advanced topics and solve tricky problems easily.

What Is Cube?

A cube is a special three-dimensional (3D) solid shape. All its six faces are equal-sized perfect squares, all sides and angles are equal, and every corner (vertex) is identical. Cubes appear in topics like geometry, mensuration (calculating area/volume), and algebraic identities (ex: a cube b cube formula).

Key Formula for Cube

Here’s the standard formula:

• Volume of a cube: $$V = a^3$$ , where a is the length of any side.
• Surface area of a cube: $$S = 6a^2$$

Cross-Disciplinary Usage

Cube is not only useful in Maths but also plays an important role in Physics, Computer Science (like data storage, graphics), architecture, and logical reasoning. Students preparing for JEE, Olympiads, and board exams will regularly see problems involving cubes.

Step-by-Step Illustration

1. Suppose the length of the side of a cube is 5 cm.
   
   To find its volume, use $$V = a^3$$ :
   $$V = 5^3 = 125$$ cubic cm.
   
   
2. To find its surface area, use $$S = 6a^2$$ :
   
   $$S = 6 \times (5^2) = 6 \times 25 = 150$$ sq. cm.
   
   

Speed Trick or Vedic Shortcut

Here’s a quick shortcut to mentally calculate the cube of any number ending with 5:

Example Trick: To quickly find the cube of 15, do this:

1. Take 1 (number before 5).
   
   Cube it: $$1^3 = 1$$
   
   
2. Multiply by the next integer: $$1 \times 2 = 2$$
3. Add a "5" at the end, get three digits: 3375 (real answer, by actual multiplication, is $$15^3 = 3375$$ ).

This trick is especially handy in mental maths rounds of school quizzes and Olympiads. Vedantu’s maths sessions cover more speed cubes and shortcuts for all classes.

Try These Yourself

• Write the cube of 2, 3, 4, 5, and 6.
• What is the surface area of a cube with side 7 cm?
• If a cube’s volume is 64 cm³, what is the length of its side?
• Name three real-life objects in the shape of a cube.

Frequent Errors and Misunderstandings

• Confusing cube with cuboid (all sides of a cube are equal; a cuboid has rectangular faces which may not be equal).
• Using $$a^2$$ (square) instead of $$a^3$$ (cube) for volume.
• Not multiplying by 6 for total surface area.
• Units mistake—using cm instead of cm³ for volume.

Relation to Other Concepts

The idea of cube connects closely with cuboid and square. Mastering cubes helps students easily move to advanced geometry, 3D visualization, and understanding algebraic cube identities.

Classroom Tip

A quick way to remember a cube’s volume is “side times side times side”—that’s why it’s called ‘cube’. Vedantu’s teachers often use models (like dice and toy boxes) in class for visual clarity.

We explored cube—from definition, formula, worked examples, common errors, relations, and tricks. Continue practicing cubes with Vedantu for strong fundamentals in geometry and algebra, which will help in your exams and higher studies!

• Cuboid and Cube: Key Differences
• Cubes and Cube Roots
• Perfect Cube of Numbers
• Volume of Cube, Cuboid and Cylinder
• Area of Square Using Diagonal