Calculate Surface Area: Finding Total Area of a 6 cm Cube

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

A cube has 6 identical square faces - top, bottom, front, back, left, and right. Since each face has the same area, we calculate one face area and multiply by 6!

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 space inside the cube. Surface area uses $ 6a^2 $, volume uses $ a^3 $.

Q: Can I just add up all six face areas separately?

Yes! You could calculate $ 36 + 36 + 36 + 36 + 36 + 36 = 216 $ cm², but using the formula $ 6a^2 $ is much faster and less prone to errors.

Q: What if the edge length has different units?

The surface area will be in square units of whatever the edge measurement uses. If edge is in meters, surface area is in m². If edge is in feet, surface area is in ft².

Q: How can I remember the surface area formula?

Think: "6 faces, each face is a² area" so total is $ 6a^2 $. Or remember cubes have 6 faces and each face is a square with area edge × edge!

Surface Area Calculation with Cube Formula

A cube has edges measuring 6 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 Edge length according to the given data

00:06 We'll use the formula for calculating cube surface area

00:10 6 times the edge length squared

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

00:16 Let's calculate 6 squared

00:22 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

A cube has edges measuring 6 cm.

Calculate the surface area of the cube.

Step-by-step solution

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

Step 1: Identify the given edge length of the cube.
Step 2: Apply the surface area formula for a cube.
Step 3: Calculate the surface area using the given edge length.

Now, let's work through each step:
Step 1: The edge length of the cube is given as $6$ cm.
Step 2: We'll use the formula for the surface area of a cube: $S = 6a^2$ , where $a$ is the edge length.
Step 3: Plugging in the value, we calculate: $S = 6 \times 6^2 = 6 \times 36 = 216$ cm².

Therefore, the surface area of the cube is $216$ cm².

Final Answer

$216$ cm².

Key Points to Remember

Essential concepts to master this topic

Formula: Surface area of cube equals 6 times edge length squared
Technique: Calculate $S = 6 \times 6^2 = 6 \times 36 = 216$ cm²
Check: Verify by counting 6 faces, each with area 36 cm² ✓

Common Mistakes

Avoid these frequent errors

Using edge length instead of edge squared
Don't calculate 6 × 6 = 36 cm² as final answer! This only gives you the area of ONE face, not all six faces. Always remember to square the edge length first, then multiply by 6 for all faces.

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

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

A cube has 6 identical square faces - top, bottom, front, back, left, and right. Since each face has the same area, we calculate one face area and multiply by 6!

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 space inside the cube. Surface area uses $6a^2$ , volume uses $a^3$ .

Can I just add up all six face areas separately?

Yes! You could calculate $36 + 36 + 36 + 36 + 36 + 36 = 216$ cm², but using the formula $6a^2$ is much faster and less prone to errors.

What if the edge length has different units?

The surface area will be in square units of whatever the edge measurement uses. If edge is in meters, surface area is in m². If edge is in feet, surface area is in ft².

How can I remember the surface area formula?

Think: "6 faces, each face is a² area" so total is $6a^2$ . Or remember cubes have 6 faces and each face is a square with area edge × edge!

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