Calculate the Surface Area of a Cube with 4cm Edges: Complete Solution

Q: Why do I multiply by 6 instead of just finding one square's area?

A cube is a 3D shape with 6 faces: top, bottom, front, back, left side, and right side. You need to add up the area of all 6 faces to get the total surface area!

Q: What's the difference between area and surface area?

Area is for flat shapes (like one square face = 16 cm²). Surface area is for 3D shapes - it's the total area of all outer surfaces combined (96 cm² for this cube).

Q: Can I use this same formula for any cube?

Yes! The formula $ A = 6s^2 $ works for any cube, no matter the edge length. Just replace 's' with your cube's edge measurement.

Q: How do I remember that a cube has 6 faces?

Think of a dice! It has 6 sides you can see: top, bottom, front, back, left, right. Each face is a perfect square in a cube.

Q: What if I get a different answer when I calculate?

Double-check your steps: Edge length squared: $ 4^2 = 16 $Multiply by 6 faces: $ 6 \times 16 = 96 $Don't forget the units: cm²

Surface Area with Six-Face Formula

A cube has edges measuring 4 cm long.

Calculate the surface area of the cube.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Calculate the surface area of the cube

00:03 Edge length according to the given data

00:06 Use the formula to calculate cube surface area

00:10 6 times the edge squared

00:13 Substitute the edge length and solve for surface area

00:17 Calculate 4 squared

00:22 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

A cube has edges measuring 4 cm long.

Calculate the surface area of the cube.

Step-by-step solution

In order to find the surface area of the cube, we need to understand that a cube has 6 identical square faces.

The formula for the surface area of a cube is given by:

$A = 6s^2$

where $s$ is the length of an edge of the cube.

According to the problem, each edge of the cube is 4 cm long. We can substitute this value into the formula:

$A = 6 \times (4)^2$

This simplifies to:

$A = 6 \times 16$

Performing the multiplication gives us:

$A = 96$

Thus, the total surface area of the cube is $96 \, \text{cm}^2$ .

Therefore, the correct answer is $\text{96 cm}^2$ , which corresponds to choice 2.

Final Answer

$96$ cm².

Key Points to Remember

Essential concepts to master this topic

Cube Structure: A cube has 6 identical square faces
Formula Application: Use $A = 6s^2$ where s = 4 gives $6 \times 16 = 96$
Verification: Count all faces: top + bottom + front + back + left + right = 6 faces ✓

Common Mistakes

Avoid these frequent errors

Calculating area of only one face
Don't find just one face area (4² = 16) and think that's the answer = 16 cm²! This ignores the other 5 faces of the cube. Always multiply the area of one face by 6 to get the total surface area.

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 do I multiply by 6 instead of just finding one square's area?

A cube is a 3D shape with 6 faces: top, bottom, front, back, left side, and right side. You need to add up the area of all 6 faces to get the total surface area!

What's the difference between area and surface area?

Area is for flat shapes (like one square face = 16 cm²). Surface area is for 3D shapes - it's the total area of all outer surfaces combined (96 cm² for this cube).

Can I use this same formula for any cube?

Yes! The formula $A = 6s^2$ works for any cube, no matter the edge length. Just replace 's' with your cube's edge measurement.

How do I remember that a cube has 6 faces?

Think of a dice! It has 6 sides you can see: top, bottom, front, back, left, right. Each face is a perfect square in a cube.

What if I get a different answer when I calculate?

Double-check your steps:

Edge length squared: $4^2 = 16$
Multiply by 6 faces: $6 \times 16 = 96$
Don't forget the units: cm²

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