Cube and Cuboid are the most used 3-D shapes in geometry. Cube and cuboid both have 6 faces, 12 edges, and 8 vertices. There are various examples of cubes and cuboids in real life like matchboxes, dice, a box, etc.

In this article, we will learn about cubes and cuboids in detail with their formulas for area and volume as well as diagonals. It also covers the properties of cubes and cuboids along with the solved examples. Let’s start our learning on the topic of Cubes and Cuboid.

What is Cube and Cuboid?

Cube and Cuboid are two three-dimensional shapes that have plane surfaces. Both Cubes and Cuboids have 6 faces, 8 vertices, and 12 edges with the difference that cubes have square faces and cuboids have rectangular faces. Let’s learn the definitions of cubes and cuboids.

Cube Definition

Cube is a three-dimensional shape that is an extension of the square. In the cube, all the sides are of equal length. A cube consists of 6 faces, 12 edges, 8 vertices, 12 face diagonals and 4 space diagonals. In other words, the shape with equal length, breadth and height is called as a cube. Some of the real-life examples of cube include a dice.

Cuboid Definition

Cuboid is the three-dimensional shape which is an extension of the rectangle. In the cuboid all the sides are length, breadth and height. A cuboid consists of 6 faces, 12 edges, 8 vertices, 12 face diagonals and 4 space diagonals. In other words, the shape with different length, breadth and height is called as a cuboid. Some of the real-life examples of cuboid include a matchbox.

Examples of Cube and Cuboid

There are multiple examples of cube and cuboid in our real-life. Some examples of cube includes a dice, a box etc. Some examples of cuboid includes matchbox, cuboidal box etc.

Cube and Cuboid Formulas

The different formulas for cube and cuboid including area, and volume; are discussed below in detail.

Surface Area of Cube

Surface Area of the cube can be classified into two:

• Lateral Surface Area
• Total Surface Area

Lateral Surface Area (LSA)

The lateral surface area of the cube is determined by adding the surface area of the faces excluding the top and bottom faces. The formula for the lateral surface area of the cube is given by:

LSA of cube = 4a²

where, a is the side of cube.

Total Surface Area (TSA)

The total surface area of the cube is determined by adding the surface area of all the faces. The formula for the total surface area of the cube is given by:

TSA of cube = 6a²

where, a is the side of cube.

Surface Area of Cuboid

Surface Area of the cuboid can be classified into two:

• Lateral Surface Area
• Total Surface Area

Lateral Surface Area (LSA) of Cuboid

The lateral surface area of the cuboid is determined by adding the surface area of the faces excluding the top and bottom faces. The formula for the lateral surface area of the cuboid is given by:

LSA of cuboid = 2h(l + b)

where,

• l is the length of cuboid,
• b is the breadth of the cuboid
• h is height of cuboid.

Total Surface Area (TSA) Cuboid

The total surface area of the cuboid is determined by adding the surface area of all the faces. The formula for the total surface area of the cuboid is given by:

TSA of cuboid = 2( lb + lh + bh)

where,

• l is the length of cuboid,
• b is the breadth of the cuboid
• h is height of cuboid.

Volume of Cube and Cuboid

Volume is the amount of space occupied by a geometrical shape. Volume in simple terms means the capacity of a solid. The formula to calculate volume of cube and cuboid is discussed below:

Volume of Cube

The volume of a cube is defined by the space bounded by all the sides of the cube. The formula for the volume of the cube is given by:

Volume of cube = a³

where, a is the side of the cube.

Volume of Cuboid

The volume of a cuboid is defined by the space bounded by all the sides of the cuboid. The formula for the volume of cuboid is given by:

Volume of cuboid = l × b × h

• where, l is the length of cuboid
• b is the breadth of the cuboid
• h is height of cuboid.

Diagonal of Cube and Cuboid Formula

The diagonal in a cube and cuboid is a line segment that joins the two opposite vertices of a face or two opposite vertices of the body. Based on this there are two types of diagonals Face Diagonals and Body Diagonals. Let’s learn this in detail

Diagonal of Cube Formula

The formula for Diagonal of Cube is mentioned below:

Face Diagonal of Cube = √2 × side

Body Diagonal of Cuboid = √3 × side

Diagonal of Cuboid Formula

The formula for Diagonal of Cuboid is mentioned below:

Face Diagonal of Cuboid = √{(side₁)² + (side₂)²}

Body Diagonal of Cuboid = √(l² + b² + h²)

Properties of Cube and Cuboid

Cube and Cuboid possess some significant properties. These properties are discussed in detail below:

Properties of Cube

There are several properties of cube some of these are listed below:

• Cube is the 3-D figure of square.
• All faces of the cube are square in shape.
• Opposite faces are parallel to each other.
• The length of all the edges is equal.
• The sides of the cube intersect each other at right angles.
• The faces of the cube meet each other at right angles.
• The space diagonals of the cube are equal.

Properties of Cuboid

There are several properties of cuboid some of these are listed below:

• Cuboid is the 3-D figure of rectangle.
• All the faces of the cuboid are rectangle in shape.
• Opposite faces and opposite edges are parallel and equal.
• The angles of the cuboid intersect at right angles.

Cube and Cuboid Difference

The main difference between cube and cuboid is tabulated below: