Geometric Classification: Analyzing the Cube-Cuboid Relationship in 3D Shapes

Shape Classification with Special Cases

Given the cube

Is each cube an cuboid?

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Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Given the cube

Is each cube an cuboid?

2

Step-by-step solution

To determine if each cube is a cuboid, we start by defining both shapes.

  • A cuboid is a three-dimensional geometric figure with six faces that are rectangles. All angles are right angles, and opposite faces are equal.
  • A cube is a special type of cuboid where all six faces are squares of equal size, meaning all sides (edges) of the cube are of equal length.

Since a cube meets all the criteria of a cuboid (having six rectangular, or in this case square, faces, with all angles being right angles), a cube can indeed be classified as a cuboid.
In mathematical terms, a cube is a specific case of a cuboid where the length, width, and height are all the same.

Therefore, the answer to the question “Is each cube a cuboid?” is Yes.

3

Final Answer

Yes

Key Points to Remember

Essential concepts to master this topic
  • Definition: A cuboid has six rectangular faces with right angles
  • Special Case: Cubes are cuboids where all faces are equal squares
  • Check: Verify cube has six faces, all rectangles (squares), all right angles ✓

Common Mistakes

Avoid these frequent errors
  • Thinking cubes and cuboids are completely different shapes
    Don't assume cubes and cuboids are separate categories = missing the relationship! This leads to incorrect classification. Always remember that cubes are a special type of cuboid where all dimensions are equal.

Practice Quiz

Test your knowledge with interactive questions

Identify the correct 2D pattern of the given cuboid:

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FAQ

Everything you need to know about this question

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

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A cube is actually a special type of cuboid! While a cuboid can have different length, width, and height, a cube has all three dimensions equal. Think of it like squares and rectangles - all squares are rectangles, but not all rectangles are squares.

How can a cube be a cuboid if they look different?

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They look different because a cube is more symmetrical, but it still meets all the requirements of a cuboid:

  • Six faces
  • All faces are rectangles (squares are special rectangles)
  • All angles are 90 degrees

Are there any cuboids that are NOT cubes?

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Yes! Most cuboids are not cubes. Examples include shoe boxes, books, and rectangular prisms where the length, width, and height are different from each other.

Why do we need to know this relationship?

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Understanding that cubes are special cuboids helps you classify shapes correctly and solve geometry problems. It's like knowing that all squares are rectangles - it prevents confusion and helps you apply the right formulas!

What makes a face rectangular in a cuboid?

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A rectangular face has four sides where opposite sides are equal and all corners are 90-degree angles. In cubes, these rectangles happen to be squares because all four sides are equal.

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