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JEE Main 2026 Preparation: Question Papers, Solutions, Mock Tests & Strategy Unacademy » JEE Study Material » Mathematics » Cuboid & Cube

Cuboid & Cube

Cuboid is the form that we're looking at here! A cube is a 3D form that may be found in items such as ice, dice, and the Rubik's cube, amongst many others. In actuality, a cube is a specific sort of cuboid in which all of the sides are squares and identical in size and shape.

Table of Content
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3D forms with six faces, eight vertices, and twelve edges are called cuboids & cubes. Cuboids & cubes are fundamental 3-dimensional objects with six faces, eight vertices, and twelve edges. On the other hand, cubes are the 3D extension of a square, but cuboids have varied lengths on each of their sides. It follows that they have different sizes in terms of both areas and volumes.  Both a cuboid and cube have right angles at their intersections. Despite the fact that both the cuboid and the cube are three-dimensional shapes, there are some differences between them. A cube’s faces are square in form, but the faces of a cuboid are rectangular in shape. 

What is Cuboid?

Rectangular faces constitute a cuboid, a three-dimensional shape with rectangular proportions. Box-shaped cuboids are known as cuboids. There are 12 sides and 8 vertices to a cuboid. The cuboid’s faces and edges aren’t equal. On the other hand, the cuboid’s opposing faces are equal. L for length; B for breadth; H for height.

 L=b=h

The bottom face of the cuboid may be any face, while the other four neighboring faces are referred to as the cuboid’s lateral faces.

Characteristics of Cuboid

  • A cuboid is a solid cube with six parallel sides.

  • Both sides of the cuboid face the same distance from the Centre.

  • A cuboid’s opposite edges are equal.

  • The vertex of a cuboid is formed by the point where three faces meet.

  • Cuboid’s angles are at 90 degrees.

how to make a cube and cuboid 

There are four sides to a cuboid and the corners or vertices are all 90 degrees. Another thing to note is that both faces are equal. A book, for instance, may be thought of as a cuboid. It features six surfaces, each with the identical proportions on both sides. While walking around your home, you’ll likely notice a number of things that have the form of a rectangular box, such as bookshelves and cabinets. Examples of rectangular-shaped items include furniture, books, and televisions. 

What is a Cube?

A cube is a three-dimensional object that is created when six identical squares bind together in an enclosed configuration. There are eight vertices and six faces in a cube. That is to say, a cube is a cuboid whose three dimensions are all the same. a cube is a three-dimensional object made up of square-shaped faces that are of the same height. A cube’s axis intersects at 90o. A cube contains six equal faces, all of which are squares. It has eight vertices and twelve identical edges.

  • Faces – 6 faces

  • Vertices – 8 vertices

  • Edges – 12 edges

Characteristics of Cube

  • All the sides of a cube are square.

  • There is no difference between the faces and edges of anything.

  • As a result, the cube’s edges are all at 90 degrees.

  • It’s a four-way match between each face and the four neighboring faces.

  • The three faces and three edges of each of the vertices are connected to one another.

  • Similarly, the edges that face each other are both parallel and equal.

Surface Area of Cylinder

In geometry, the surface area of a cylinder is defined as the entire space covered by the flat surfaces of the cylinder’s bases, together with the curved surface of the cylinder. Each of the cylinder’s two components contributes to the overall surface area: one curved surface area and two flat surface areas. 

Surface Area of a Cylinder Calculated Using a Formula 

It is necessary to apply the formula for the surface area of the cylinder in order to determine the surface area occupied by the bases of the cylinder as well as by the curved surface of the cylinder. Because a cylinder has a curved surface, we may express the curved surface area of the cylinder as well as the overall surface area of the cylinder. There are two types of surface areas on a cylinder: the Total Surface Area and the Curved Surface Area. 

Using the following formulae, given that the radius of a cylinder’s base is “r” and that the height of a cylinder is “h,” the surface area of a cylinder may be calculated as follows: 

  • a measure of the total surface area T = 2πr(r + h)

  • Surface Area with a Curve , S = 2πrh

cube cuboid and cylinder formula

Cuboid

Cube

Cylinder

Total Surface Area = 2(LB+BH+LH)

Total surface area = 6 (a*a)

Total surface area  2πr(r + h)

Volume = L×BH

Volume = a×aa

 

Lateral surface area = 2H(LB)

Lateral surface area = 4(aa)

Curved surface area  2πrh

Perimeter=4(L+B+H)

Diagonal = 3a

 

Diagonal = {(LL)+(BB)+(HH)}

Perimeter = 12a

 

Cuboid vs. Cube?

S.No

Cuboid

Cube

1

The length, width, and height of a cuboid are not all equal.

The length, width, and height of a cube are all the same, i.e. all the edges are equal.

2

A rectangle in three dimensions is known as a “cuboid.”

A square in three dimensions is known as a “cube.”

3

Each of the cuboid’s six sides is a rectangle.

Each of the cube’s six sides is a square.

4

It has 12 diagonals. However, three of the four diagonals in the set have different lengths.

There are exactly the same number of equal-sized diagonals over the whole surface. 

5

There are 4 internal diagonals to this structure. It’s only that the two pairs have a different length

The four internal diagonals are all the same length. 

6

Cuboids include objects like Bricks and Duster.

Ice cubes, dice, and Rubik’s cubes are all examples of cubes.

Conclusion

In contrast to the cube, which has all of its edges (sides) of equal length, the edges of a cuboid are all of varying lengths. For comparison, all sides of the cube are of the square form, but all of the sides of the cuboid are of the rectangular shape. A cube’s surface area is equal on all of its faces, but a cuboid’s surface area is equal only on the opposing faces of the cuboid. The diagonals of a cube are all equal, but the diagonals of parallel sides of a cuboid are the only ones that are equal to one another.

 
faq

Frequently asked questions

Get answers to the most common queries related to the IIT JEE Examination Preparation.

Are all of the diagonals of a cuboid of the same length?

Ans.  No. Only the diagonals that are opposing and parallel are equal.

What are some alternative names for a cuboid?

Ans.  A cuboid is also known by other names, such as rectangle prism, right prism, and rectangular parallelepiped, ...Read full

What are some alternative names for a cube?

Ans. Cubes are three-dimensional objects formed when six identical squares are joined together in an enclosed arrang...Read full

Is it possible to refer to a cube as a cuboid?

Ans. It is true that the cube is a specific kind of cuboid in which all of the cuboid faces have the same length. De...Read full

What is the formula for calculating the perimeters of a cube and a cuboid?

Ans. The circumference of a cube is equal to 12a. The perimeter of a cuboid is equal to 4(L + B + H). ...Read full

Ans.  No. Only the diagonals that are opposing and parallel are equal.

Ans.  A cuboid is also known by other names, such as rectangle prism, right prism, and rectangular parallelepiped, which all refer to its shape.

Ans. Cubes are three-dimensional objects formed when six identical squares are joined together in an enclosed arrangement to form a solid item. A cube has eight vertices and six faces, making it a four-sided shape. To put it another way, a cube is a cuboid whose three dimensions are all the same size and shape. In three-dimensional geometry, a cube is a solid object made up of square-shaped faces that are all the same height. The axis of a cube crosses at a 90-degree angle. A cube has six equal faces, all of which are squares, which make up the shape of the cube. It contains eight vertices and twelve edges that are similar to one another. A cube is also known by other names, such as hexahedron, square block, 6-sided solid, and so on, although the most common is cube.

Ans. It is true that the cube is a specific kind of cuboid in which all of the cuboid faces have the same length. Despite the fact that at first sight both the cuboid and the cube seem to have the same shape; they have distinct features that set them apart. The cube and cuboid are both geometric shapes.

Ans. The circumference of a cube is equal to 12a. The perimeter of a cuboid is equal to 4(L + B + H).

 

 

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