Calculate the Surface Area of a Cube with 8 cm Edges: Geometry Problem

Q: Why do we multiply by 6 in the surface area formula?

A cube has 6 faces - top, bottom, front, back, left, and right. Each face is a square with the same area, so we calculate one face area and multiply by 6 to get the total surface area.

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

Surface area measures the total area of all outside faces (like wrapping paper needed). Volume measures the space inside the cube. Surface area uses $ 6a^2 $, volume uses $ a^3 $.

Q: How can I visualize this problem better?

Imagine unfolding a cube into a flat cross shapeYou'll see 6 identical squares, each $ 8 \times 8 = 64 $ cm²Add them up: 6 × 64 = 384 cm²

Surface Area Formula with 3D Visualization

A cube has edges measuring 8 cm.

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 The edge length according to the given data

00:07 We'll use the formula for calculating cube surface area

00:10 6 times the edge squared

00:13 We'll substitute the edge length and solve for the surface area

00:17 Calculate 8 squared

00:24 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 8 cm.

Calculate the surface area of the cube.

Step-by-step solution

To calculate the surface area of the cube, follow these steps:

Step 1: Apply the appropriate formula. The formula for the surface area of a cube is $S = 6a^2$ , where $a$ is the edge length.
Step 2: Substitute the given values into the formula. In this problem, $a = 8$ cm.
Step 3: Perform the calculation. Replace $a$ in the formula: $\begin{aligned} S = 6 \times (8 \, \text{cm})^2 = 6 \times 64 \, \text{cm}^2 = 384 \, \text{cm}^2 \end{aligned}$

Thus, the surface area of the cube is $\mathbf{384 \, \text{cm}^2}$ .

Finally, comparing the result to the given choices, choice 1 is correct: $384$ .

Final Answer

$384$ cm².

Key Points to Remember

Essential concepts to master this topic

Formula: Surface area of cube = $6a^2$ where a is edge length
Technique: Calculate $6 \times 8^2 = 6 \times 64 = 384$ cm²
Check: Count 6 faces each with area 64 cm²: 64 + 64 + 64 + 64 + 64 + 64 = 384 ✓

Common Mistakes

Avoid these frequent errors

Forgetting to multiply by 6 faces
Don't just calculate $8^2 = 64$ cm² and stop there = only one face area! This gives you the area of just one square face, not the entire surface. Always multiply by 6 since a cube has 6 identical square faces.

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 we multiply by 6 in the surface area formula?

A cube has 6 faces - top, bottom, front, back, left, and right. Each face is a square with the same area, so we calculate one face area and multiply by 6 to get the total surface area.

What's the difference between surface area and volume?

Surface area measures the total area of all outside faces (like wrapping paper needed). Volume measures the space inside the cube. Surface area uses $6a^2$ , volume uses $a^3$ .

Do I need to memorize the surface area formula?

It helps, but you can also think logically! A cube has 6 square faces, each with area $a^2$ . So total surface area = 6 × area of one face = $6a^2$ .

What if the edge length has different units?

The formula works the same way! Just remember that surface area will have square units. If edge = 5 meters, then surface area = $6 \times 5^2 = 150$ square meters.

How can I visualize this problem better?

Imagine unfolding a cube into a flat cross shape
You'll see 6 identical squares, each $8 \times 8 = 64$ cm²
Add them up: 6 × 64 = 384 cm²

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