Calculate Total Edge Length: 4cm Cube Geometry Problem

Q: Why does a cube have exactly 12 edges?

A cube has 8 vertices (corners) and each vertex connects to 3 edges. That gives 8 × 3 = 24, but each edge connects 2 vertices, so we divide by 2: $ \frac{24}{2} = 12 $ edges total.

Q: How can I visualize all 12 edges if some are hidden?

Think of a cube as having 4 edges on top, 4 on bottom, and 4 vertical edges connecting them. Even if you can't see all edges in a 2D drawing, they're all there in the 3D shape!

Q: Is there a faster way than counting edges?

Yes! Just remember the formula: Total edge length = 12 × side length. For any cube problem, multiply the side length by 12 and you're done.

Q: How is this different from finding the perimeter of a square?

A square has 4 edges (perimeter = 4 × side), but a cube is 3D with 12 edges. Don't confuse 2D shapes with 3D shapes - they have different edge counts!

Cube Edge Length with Multiplication Strategy

Shown below is a cube with a length of 4 cm.

What is the sum of the lengths of the cube's edges?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find the sum of the cube's edge lengths

00:03 In a cube all edges are equal, let's mark it with A

00:06 Let's find them all

00:21 Multiply the number of edges by the edge length according to the given data

00:29 Let's calculate and solve

00:35 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

Shown below is a cube with a length of 4 cm.

What is the sum of the lengths of the cube's edges?

Step-by-step solution

To find the sum of the lengths of all the edges of a cube, we can follow these steps:

Step 1: Recognize that a cube has 12 edges, and each edge is the same length.
Step 2: Given the side length of the cube is 4 cm, use the formula for the total edge length.

The formula for the total length of the edges of a cube is:

$\text{Total length} = \text{number of edges} \times \text{length of one edge}$

Substituting the known values, we have:

$\text{Total length} = 12 \times 4 \, \text{cm}$

Calculating this gives:

$\text{Total length} = 48 \, \text{cm}$

Therefore, the sum of the lengths of the cube's edges is $48 \, \text{cm}$ .

Final Answer

$48$

Key Points to Remember

Essential concepts to master this topic

Cube Structure: Every cube has exactly 12 edges of equal length
Formula: Total edge length = 12 × side length = 12 × 4 = 48 cm
Verification: Count visible edges (9) plus hidden edges (3) equals 12 total ✓

Common Mistakes

Avoid these frequent errors

Counting only visible edges instead of all 12 edges
Don't count just the 9 visible edges you can see in the diagram = wrong total of 36 cm! The 3 hidden edges behind the cube are still part of its structure. Always remember a cube has exactly 12 edges total, whether visible or not.

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?

A cube has 8 vertices (corners) and each vertex connects to 3 edges. That gives 8 × 3 = 24, but each edge connects 2 vertices, so we divide by 2: $\frac{24}{2} = 12$ edges total.

How can I visualize all 12 edges if some are hidden?

Think of a cube as having 4 edges on top, 4 on bottom, and 4 vertical edges connecting them. Even if you can't see all edges in a 2D drawing, they're all there in the 3D shape!

Is there a faster way than counting edges?

Yes! Just remember the formula: Total edge length = 12 × side length. For any cube problem, multiply the side length by 12 and you're done.

What if the cube had a different side length?

The method stays the same! If the side length was 5 cm, the total would be $12 \times 5 = 60$ cm. The number of edges (12) never changes for a cube.

How is this different from finding the perimeter of a square?

A square has 4 edges (perimeter = 4 × side), but a cube is 3D with 12 edges. Don't confuse 2D shapes with 3D shapes - they have different edge counts!

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