Cuboid Dimensions Analysis: Comparing Height and Length in 3D Shapes

Q: Can a cuboid be taller than it is long?

Absolutely! In a cuboid, the height can be greater than, less than, or equal to the length. There are no restrictions on which dimension must be largest.

Q: How do I identify if a 3D shape is a cuboid?

Look for six rectangular faces where opposite faces are identical and parallel. If all faces are squares, it's specifically a cube (a special cuboid).

Q: Are there real-world examples of cuboids with different dimensions?

Yes! Think of a shoebox (longer than tall), a bookcase (taller than wide), or a laptop (wider than thick). Most rectangular objects around us are cuboids, not cubes.

Cuboid Properties with Dimensional Variations

Look at the cube below.

Can a cuboid have a height that is different to its length?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Is there a box where the height is different from the length?

00:03 In a cube, all edges are equal

00:07 Therefore, in a cube, the height and length must be equal

00:12 Let's draw a box

00:23 In a box, not all edges are necessarily equal

00:27 Therefore, the height and length can also be different

00:30 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Look at the cube below.

Can a cuboid have a height that is different to its length?

Step-by-step solution

To solve this problem, we'll clarify the definitions and properties of a cuboid:

A cuboid is a three-dimensional geometric figure with six rectangular faces, where opposite faces are equal and parallel. Importantly, a cuboid has dimensions that are specified as length, width, and height, and these values can be different from one another.
A cube is a special type of cuboid where all three dimensions (length, width, and height) are equal. This makes all faces of a cube identical squares.

Given these definitions, we analyze the problem:

Since a cuboid's dimensions can be different, it follows that the height of a cuboid can indeed be different from its length. This contrasts with a cube where all dimensions must be equal.

Hence, we conclude that it is possible for a cuboid to have a height that is different from its length.

Therefore, the answer to the question is Yes.

Final Answer

Yes.

Key Points to Remember

Essential concepts to master this topic

Definition: A cuboid can have three different dimensions unlike cubes
Technique: Compare rectangular faces - length, width, height can all vary
Check: Verify if all dimensions equal then it's a cube ✓

Common Mistakes

Avoid these frequent errors

Confusing cuboids with cubes
Don't assume all 3D rectangular shapes must have equal dimensions = wrong classification! This confuses cuboids (which can have different length, width, height) with cubes (which must have all equal sides). Always remember cuboids allow dimensional variation while cubes require all dimensions to be identical.

Practice Quiz

Test your knowledge with interactive questions

A cube has a total of 14 edges.

FAQ

Everything you need to know about this question

What's the difference between a cube and a cuboid?

A cube is a special type of cuboid where all three dimensions are equal. A cuboid can have different length, width, and height measurements.

Can a cuboid be taller than it is long?

Absolutely! In a cuboid, the height can be greater than, less than, or equal to the length. There are no restrictions on which dimension must be largest.

How do I identify if a 3D shape is a cuboid?

Look for six rectangular faces where opposite faces are identical and parallel. If all faces are squares, it's specifically a cube (a special cuboid).

Are there real-world examples of cuboids with different dimensions?

Yes! Think of a shoebox (longer than tall), a bookcase (taller than wide), or a laptop (wider than thick). Most rectangular objects around us are cuboids, not cubes.

Does the orientation change whether it's a cuboid?

No! Whether you place a cuboid on its side, end, or any face, it's still the same cuboid. The shape itself determines if it's a cuboid, not how it's positioned.

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