Cube Edge Count: Investigating the Claim of 14 Edges

Cube Properties with Edge Counting

A cube has a total of 14 edges.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Are there a total of 14 edges in a cube?
00:03 An edge is a line segment in a cube
00:07 Let's mark all the edges and count them
00:25 We can see that we have 12 edges in a cube
00:32 And this is the solution to the question

Step-by-step written solution

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1

Understand the problem

A cube has a total of 14 edges.

2

Step-by-step solution

To solve this problem, we'll analyze the basic properties of a cube as follows:

  • Step 1: Recall that a cube has 6 faces, 12 edges, and 8 vertices.
  • Step 2: Crucially, each face of a cube is a square, and a cube has exactly three edges meeting at each vertex.
  • Step 3: Count the edges: A cube's geometry dictates that it has 12 edges since each cube has 4 edges per face, shared equally among its 6 square faces.

Now, let's perform a check by thinking through the geometry:

A cube consists of 66 faces and each face shares its edges with adjacent faces. The twelve unique edges appear as 6×4÷26 \times 4 \div 2 edges (since each edge is counted twice, once on each adjoining face).

Thus, it is evident that a cube has exactly 12 edges, not 14.

Therefore, the statement that a cube has 14 edges is False.

3

Final Answer

False.

Key Points to Remember

Essential concepts to master this topic
  • Cube Structure: 6 faces, 12 edges, 8 vertices always
  • Counting Method: Each edge shared by 2 faces, so 6×4÷2=12 6 \times 4 \div 2 = 12
  • Verification: Count by tracing edges systematically around the cube ✓

Common Mistakes

Avoid these frequent errors
  • Double-counting shared edges
    Don't count each edge separately for every face it belongs to = 24 edges instead of 12! This counts every edge twice since each edge touches exactly 2 faces. Always remember edges are shared between adjacent faces.

Practice Quiz

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A cube has a total of 14 edges.

FAQ

Everything you need to know about this question

Why does a cube have exactly 12 edges?

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A cube has 6 square faces, and each square has 4 edges. But since adjacent faces share edges, we calculate: 6×4÷2=12 6 \times 4 \div 2 = 12 edges total.

How can I visualize the 12 edges?

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Think of a cube as having 4 edges on top, 4 edges on bottom, and 4 vertical edges connecting the top and bottom faces. That's 4 + 4 + 4 = 12!

What's the difference between edges and vertices?

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Edges are the lines where two faces meet (12 total). Vertices are corner points where edges meet (8 total). Don't confuse these two different parts!

Does the size of the cube change the number of edges?

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No! Whether it's a tiny cube or huge cube, the shape stays the same. All cubes have exactly 12 edges, 6 faces, and 8 vertices regardless of size.

How do I remember cube properties?

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Use Euler's formula: V - E + F = 2. For cubes: 8 - 12 + 6 = 2 ✓. This helps you remember that vertices (8), edges (12), and faces (6) are connected!

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