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

All faces of the cube must be?

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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