Calculate Surface Area: Cube with 12 cm Edges

Q: Why do I 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 area $ s^2 $, the total surface area is $ 6s^2 $.

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

Surface area measures the total area of all faces (like wrapping paper needed). Volume measures space inside (like water it can hold). Surface area uses $ 6s^2 $, volume uses $ s^3 $.

Q: Do I need to memorize the surface area formula?

It helps, but you can also think logically! Count the faces (6), find each face's area ($ s^2 $), then multiply: $ 6 \times s^2 $.

Q: What if the cube had different edge lengths?

The formula stays the same: $ A = 6s^2 $. Just substitute the new edge length for s. The key is that all edges of a cube are equal.

Q: How can I check if 864 cm² is reasonable?

Each face is $ 12^2 = 144 $ cm². With 6 faces: $ 6 \times 144 = 864 $ cm². You can also estimate: 6 × 140 ≈ 840, so 864 makes sense!

Surface Area Calculations with Cube Geometry

The edges of a cube are 12 cm long.

What is 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 Find the surface area of the cube

00:03 Edge length according to the given data

00:06 We'll use the formula to calculate the surface area of a cube

00:10 Multiply the number of faces (6) by the area of one face

00:14 Substitute appropriate values and solve to find the surface area

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

The edges of a cube are 12 cm long.

What is the surface area of the cube?

Step-by-step solution

To solve for the surface area of the cube, follow these steps:

Step 1: Identify the given information. The edge length of the cube is 12 cm.
Step 2: Apply the surface area formula for a cube, which is $A = 6s^2$ , where $s$ is the side length.
Step 3: Substitute the side length into the formula: $A = 6 \times 12^2$ .
Step 4: Calculate $12^2 = 144$ .
Step 5: Multiply the result by 6: $A = 6 \times 144 = 864$ .

Therefore, the surface area of the cube is $864 \, \text{cm}^2$ .

Final Answer

$864$ cm².

Key Points to Remember

Essential concepts to master this topic

Formula: Surface area of cube equals six times side squared
Technique: Calculate $A = 6 \times 12^2 = 6 \times 144 = 864$
Check: Count all six faces and verify each has area 144 cm² ✓

Common Mistakes

Avoid these frequent errors

Calculating area of only one face
Don't calculate just 12² = 144 and call it surface area! This gives only one face's area, missing the other five faces. Always multiply by 6 since cubes have exactly six identical square faces.

Practice Quiz

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Identify the correct 2D pattern of the given cuboid:

FAQ

Everything you need to know about this question

Why do I 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 area $s^2$ , the total surface area is $6s^2$ .

What's the difference between surface area and volume?

Surface area measures the total area of all faces (like wrapping paper needed). Volume measures space inside (like water it can hold). Surface area uses $6s^2$ , volume uses $s^3$ .

Do I need to memorize the surface area formula?

It helps, but you can also think logically! Count the faces (6), find each face's area ( $s^2$ ), then multiply: $6 \times s^2$ .

What if the cube had different edge lengths?

The formula stays the same: $A = 6s^2$ . Just substitute the new edge length for s. The key is that all edges of a cube are equal.

How can I check if 864 cm² is reasonable?

Each face is $12^2 = 144$ cm². With 6 faces: $6 \times 144 = 864$ cm². You can also estimate: 6 × 140 ≈ 840, so 864 makes sense!

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