Cuboid Shape: Definition, Shape, Formula & Solved Examples

Cuboid Shape: A cuboid three-dimensional geometrical shape. It is a convex polyhedron that consists of six rectangular faces, eight vertices, and twelve edges. It is one of the most commonly seen shapes around us. It has three dimensions namely, length (l), width (w), and height (h) Carton boxes, books, cardboards, cabinets are some examples of cuboid shapes that we use in our everyday life.

This is one of the important geometrical shapes studied by the students in their primary classes. Understanding the cuboid shape will help students to solve mathematical problems in a fraction of seconds. Therefore, you can check NCERT Solutions for Class 8 Maths Chapter 10 for a better understanding of the cuboid shape. We have provided detailed information on cuboids in this article. Read on to find out about its definition, formulas, and solved examples.

Definition of Cuboid Shape

In Mathematics, a cuboid is a convex polyhedron with six rectangular faces, eight vertices, and twelve edges. In cuboid shape, all the angles are right angles and have equal opposite faces. The line segment of the cuboid is called edges whereas the point of intersection of the cuboid is known as the vertex. We come across the shape of cuboids in our day-to-day life in the form of boxes, containers, books, cabinets, electronic devices, etc. Unlike a cube, the length, width, and height are different in cuboids. The faces of the cuboid are parallel to each other.

Properties of Cuboid

Some of the properties of a cuboid are given below:

It is a convex polyhedron shape.
It has 6 rectangular faces, 8 vertices, and 12 edges.
The dimensions of a cuboid are length (l), width (w), and height (h).
All angles formed at the vertices of a cuboid are right angles.
The faces other than the opposite faces are called adjacent faces.
Opposite edges of a cuboid are parallel to each other.

Download NCERT Solutions for Class 8 Maths Chapter 10 PDF

Cuboid Formulas

The formulas used to calculate the shape of a cuboid are mentioned below:

Measure	Formula
Lateral Surface Area (LSA) of Cuboid	2h (l + b) Square Units
Total Surface Area (TSA) of Cuboid	2(lb + bh + hl) Square Units
Volume of Cuboid	(l × b × h) Cubic Units
Diagonal of Cuboid	√(l² + b² + h²) Units

The surface area of a cuboid is the region occupied by the faces. We can say that it is the sum of all its faces. There are two types of surface area i.e., lateral surface area and total surface area.

Lateral Surface Area of Cuboid

It is the sum of four faces excluding top and bottom faces. The formula used for calculating the lateral surface area of a cuboid is as follows:

Lateral Surface Area of Cuboid = 2h (l + b) Square Units

Total Surface Area of Cuboid

It is the sum of all its rectangular faces. The formula used for calculating the total surface area of cuboid is as follows:

Total Surface Area of Cuboid = 2 (lb + bh + hl) Square Units

Volume of Cuboid

It is equal to the product of area of base and height of the cuboid. The formula used for calculating volume of cuboid is as follows:

Volume of Cuboid = (l × b × h) Cubic Units

Diagonal of Cuboid

The length of the cuboid is calculated by using the formula as given below:

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

Perimeter of Cuboid

It is the sum of all the sides of the cuboid. The formula used to calculate the perimeter of cuboid is as follows:

Perimeter of Cuboid = 4 (l + b + h) Units

Solved Examples of Cuboid Shape

Some of the solved examples of a cuboid are given below:

Example 1: Find the volume of a cuboid of length 8 cm, breadth 6 cm, and height 4 cm.

Example 1: Find the volume of a cuboid of length 8 cm, breadth 6 cm, and height 4 cm.

Solution: Given, l= 8 cm, b= 6 cm and h = 4 cm

Volume = l x b x h
= 8 x 6 x 4
=192 cm³

Therefore, the volume of the cuboid is 192 cm³

Example 2: Find the lateral and total surface area of a cuboid measuring 10 cm × 6 cm × 4 cm.

Solution: Given, l=10 cm, b=6 cm and h= 4 cm

Lateral Surface area= 2h(l + b)
= 2 x 4 (10+6)
=8 (16)= 128 cm²

Therefore, the lateral surface area of a cuboid is 128 cm²

Total Surface Area= 2(lb + bh + hl)
= 2 (10 x 6 +6 x 4+ 4 x10)
=2 (60+24+40)= 2 (124)
=248 cm²

Therefore, the total surface area of a cuboid is 248 cm²

Frequently Asked Questions on Cuboidal Shape

Some frequently asked questions on cuboid shape are given below:

Q. What is a cuboid?
A. It is a three-dimensional figure composed of six rectangular faces.

Q. What are the properties of a cuboid?
A. The cuboid has 6 faces, 8 vertex, and 12 edges.

Q. What is the formula of the total surface area of a cuboid?
A. The total surface area of a cuboid is the region occupied by its faces. It is calculated by using formula 2 (lb + bh + hl) square units.

Q. What are some real-life examples of the cuboid?
A. Some real-life examples of cuboids are cabinets, books, carton box, containers, etc.

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