Calculate Total Edge Length: 7cm Cube Edge Measurement Problem

Q: Why does a cube have 12 edges exactly?

Think of a cube as having 3 sets of 4 parallel edges: 4 edges on top face, 4 edges on bottom face, and 4 vertical edges connecting them. That's 4 + 4 + 4 = 12 edges total!

Q: Is this the same as finding the perimeter?

Not exactly! This is the total edge length of a 3D shape. Perimeter applies to 2D shapes. For cubes, we're adding up all the edges that make the wireframe structure.

Q: What's the difference between edges, faces, and vertices?

Edges are the lines where faces meet (12 total). Faces are the flat surfaces (6 total). Vertices are the corner points (8 total). This problem asks about edges!

Q: Do all the edges have to be the same length?

Yes! By definition, a cube has all edges equal in length. If the edges were different lengths, it would be a rectangular prism, not a cube.

Q: How is this different from surface area or volume?

Total edge length is 1-dimensional (just length). Surface area is 2-dimensional (area of faces). Volume is 3-dimensional (space inside). Each measures different properties!

Cube Edge Properties with Total Perimeter

Given the cube whose edge length is equal to 7 cm

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

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:07 Let's find the sum of all the cube's edge lengths.

00:10 In a cube, all the edges are the same length. Let's call that length A.

00:16 Now, let's calculate the total length of all the edges.

00:28 Multiply the number of edges by the length A.

00:32 Let's do the math and find the answer.

00:42 And that's how we solve this problem!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Given the cube whose edge length is equal to 7 cm

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

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Recall that a cube has 12 edges.
Step 2: Use the formula for the sum of the lengths of cube's edges: $12 \times \text{edge length}$ .
Step 3: Perform the calculation using the given edge length of 7 cm.

Now, let's work through each step:
Step 1: A cube has a total of 12 edges.
Step 2: Using the formula, the sum of the lengths of the edges is $12 \times 7$ .
Step 3: Calculating this gives us $12 \times 7 = 84$ cm.

Therefore, the sum of the lengths of the edges of the cube is $84$ cm.

Final Answer

$84$

Key Points to Remember

Essential concepts to master this topic

Rule: A cube has exactly 12 edges of equal length
Technique: Multiply edge length by 12: $7 \times 12 = 84$ cm
Check: Count cube edges in diagram: 4 top + 4 bottom + 4 vertical = 12 ✓

Common Mistakes

Avoid these frequent errors

Confusing edge count with face count
Don't multiply edge length by 6 (faces) = wrong answer 42! This gives the wrong total because cubes have 6 faces but 12 edges. Always remember a cube has 12 edges, not 6.

Practice Quiz

Test your knowledge with interactive questions

A cube has a total of 14 edges.

FAQ

Everything you need to know about this question

Why does a cube have 12 edges exactly?

Think of a cube as having 3 sets of 4 parallel edges: 4 edges on top face, 4 edges on bottom face, and 4 vertical edges connecting them. That's 4 + 4 + 4 = 12 edges total!

Is this the same as finding the perimeter?

Not exactly! This is the total edge length of a 3D shape. Perimeter applies to 2D shapes. For cubes, we're adding up all the edges that make the wireframe structure.

What's the difference between edges, faces, and vertices?

Edges are the lines where faces meet (12 total). Faces are the flat surfaces (6 total). Vertices are the corner points (8 total). This problem asks about edges!

Do all the edges have to be the same length?

Yes! By definition, a cube has all edges equal in length. If the edges were different lengths, it would be a rectangular prism, not a cube.

How is this different from surface area or volume?

Total edge length is 1-dimensional (just length). Surface area is 2-dimensional (area of faces). Volume is 3-dimensional (space inside). Each measures different properties!

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Cuboids questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime