102 LearnersLast updated on August 13th, 2025
Properties of Cuboid
A cuboid is a three-dimensional shape that has unique properties useful in simplifying geometric problems related to cuboids. The properties of a cuboid include having six rectangular faces, opposite faces being equal, and all angles being right angles. These properties help students analyze and solve problems related to volume, surface area, and geometry. Now, let us learn more about the properties of a cuboid.
What are the Properties of a Cuboid?
The properties of a cuboid are straightforward and help students understand and work with this type of three-dimensional shape. These properties are derived from geometric principles. There are several properties of a cuboid, and some of them are mentioned below: Property 1: Faces A cuboid has six rectangular faces. Property 2: Opposite Faces Opposite faces of a cuboid are equal. Property 3: Edges A cuboid has 12 edges, with opposite edges being equal. Property 4: Vertices A cuboid has 8 vertices. Property 5: Right Angles All the internal angles of a cuboid are right angles (90 degrees). Property 6: Volume Formula The formula used to calculate the volume of a cuboid is given below: Volume = length x width x height
Tips and Tricks for Properties of a Cuboid
Students might confuse different properties of cuboids. To avoid such confusion, we can follow the following tips and tricks: Rectangular Faces: Students should remember that all faces of a cuboid are rectangles. This is the defining feature of a cuboid. Equal Opposite Faces: Students should note that opposite faces in a cuboid are equal rectangles. Right Angles: Students should remember that all internal angles in a cuboid are right angles, ensuring that the shape is a right rectangular prism.
Confusing a Cuboid with a Cube
Students should remember that a cuboid has rectangular faces, while a cube has square faces, meaning all sides of a cube are equal.
Mistake 1
Misinterpreting the Angle Relationships
Students should remember that all angles in a cuboid are right angles, unlike other polyhedra.
Mistake 2
Incorrectly Applying the Volume Formula
Students should practice using the correct formula to find the volume of a cuboid, which is given below. They must also understand the representation of length, width, and height. Volume = length x width x height
Mistake 3
Misunderstanding the Face Relationships
Students should remember that opposite faces of a cuboid are equal rectangles.
Mistake 4
Forgetting the Rectangular Face Rule
Students must remember that all faces of a cuboid are rectangles, not necessarily squares like in a cube.
Mistake 5
Solved Examples on the Properties of Cuboids
In a cuboid, the length is 5 cm, the width is 3 cm, and the height is 4 cm. What is the volume of the cuboid?
Volume = 60 cubic cm.
Problem 1
Applying the formula, volume = length x width x height Substituting the values into the formula, we get Volume = 5 x 3 x 4 = 60 cm³.
If a cuboid has a length of 8 cm and a width of 5 cm, and the area of one of its faces is 40 cm², what is the height of the cuboid?
Explanation
Height = 5 cm
Problem 2
The area of a face of the cuboid is given by length x height, or width x height. Here, 8 x height = 40 Height = 40 / 8 = 5 cm.
A cuboid has faces with dimensions 4 cm by 3 cm, 4 cm by 2 cm, and 3 cm by 2 cm. What is the total surface area of the cuboid?
Explanation
Total surface area = 52 square cm.
Problem 3
Total surface area = 2(lw + lh + wh) Substituting the values, we get Total surface area = 2(4x3 + 4x2 + 3x2) = 2(12 + 8 + 6) = 2x26 = 52 cm².
In a cuboid, the volume is 96 cm³, with a length of 6 cm and a width of 4 cm. What is the height of the cuboid?
Explanation
Height = 4 cm
Problem 4
Volume = length x width x height 96 = 6 x 4 x height Height = 96 / 24 = 4 cm.
A cuboid has a length of 7 cm, width of 3 cm, and height of 2 cm. What is the length of the diagonal of the cuboid?
Explanation
Diagonal = 8.54 cm (approx).
A cuboid is a three-dimensional shape with six rectangular faces, with opposite faces being equal.
1.How many faces does a cuboid have?
2.Are all faces of a cuboid equal?
3.How do you find the volume of a cuboid?
4.Can a cuboid have square faces?
Common Mistakes and How to Avoid Them in Properties of Cuboids
Students may get confused while understanding the properties of a cuboid and might make mistakes while solving related problems. Here are some common mistakes students tend to make and solutions to these mistakes.
Hiralee Lalitkumar Makwana
About the Author
Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.
Fun Fact
: She loves to read number jokes and games.
