Cube Edge Count: Investigating the Claim of 14 Edges

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.

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What are the dimensions of a cuboid composed of two 4X3 rectangles

and of four 4X4 squares?

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