Calculate Total Edge Length: Cube with 6.5 cm Sides

Q: How many edges does a cube actually have?

A cube has exactly 12 edges. Think of it as 4 edges on the bottom face, 4 edges on the top face, and 4 vertical edges connecting them together.

Q: Why not multiply by 6 since a cube has 6 faces?

That would give you the total surface area if each face was 6.5 × 6.5! We want edge length, not area. Remember: 12 edges, 6 faces, 8 vertices are different properties.

Q: What if I can't see all the edges in the diagram?

Don't worry! Even if some edges are hidden in the 3D drawing, a cube always has 12 edges. The diagram shows a typical cube - trust the geometric property.

Q: Is there a formula I should memorize?

Yes! For any cube: Total edge length = 12 × (length of one edge). This works because all edges in a cube are identical.

Q: How can I double-check my multiplication?

Try breaking it down: $ 12 \times 6.5 = 12 \times 6 + 12 \times 0.5 = 72 + 6 = 78 $. Or use $ 10 \times 6.5 + 2 \times 6.5 = 65 + 13 = 78 $.

Cube Edge Properties with Length Summation

Given the cube and the length of each edge equals 6.5 cm

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

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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 as A

00:07 Let's find them all

00:20 Multiply the number of edges by the given edge length

00:27 Let's calculate and solve

00:35 And this is the solution to the problem

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Given the cube and the length of each edge equals 6.5 cm

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

Step-by-step solution

To solve this problem, we need to find the total length of all the edges of a cube where each edge measures 6.5 cm. A cube has 12 edges, and the length of each edge is identical.

We'll apply the formula for the sum of the lengths of the edges of a cube:

Formula: Total edge length = $12 \times \text{edge length}$

Substitute the given edge length into the formula:

Total edge length = $12 \times 6.5$ .

Now let's do the calculation:

Total edge length = $12 \times 6.5 = 78$ .

Therefore, the sum of the lengths of the edges of the cube is $\mathbf{78}$ cm.

The correct choice from the given options is choice 4, which corresponds to the result of $78$ .

Final Answer

$78$

Key Points to Remember

Essential concepts to master this topic

Rule: A cube has exactly 12 edges of equal length
Technique: Total edge length = $12 \times 6.5 = 78$ cm
Check: Count edges systematically: 4 bottom + 4 top + 4 vertical = 12 ✓

Common Mistakes

Avoid these frequent errors

Counting only visible edges or faces instead of total edges
Don't count just 8 visible edges or multiply by 6 faces = wrong total! This misses hidden edges or confuses edges with faces. Always remember a cube has exactly 12 edges total, regardless of viewing angle.

Practice Quiz

Test your knowledge with interactive questions

Identify the correct 2D pattern of the given cuboid:

FAQ

Everything you need to know about this question

How many edges does a cube actually have?

A cube has exactly 12 edges. Think of it as 4 edges on the bottom face, 4 edges on the top face, and 4 vertical edges connecting them together.

Why not multiply by 6 since a cube has 6 faces?

That would give you the total surface area if each face was 6.5 × 6.5! We want edge length, not area. Remember: 12 edges, 6 faces, 8 vertices are different properties.

What if I can't see all the edges in the diagram?

Don't worry! Even if some edges are hidden in the 3D drawing, a cube always has 12 edges. The diagram shows a typical cube - trust the geometric property.

Is there a formula I should memorize?

Yes! For any cube: Total edge length = 12 × (length of one edge). This works because all edges in a cube are identical.

How can I double-check my multiplication?

Try breaking it down: $12 \times 6.5 = 12 \times 6 + 12 \times 0.5 = 72 + 6 = 78$ . Or use $10 \times 6.5 + 2 \times 6.5 = 65 + 13 = 78$ .

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