Calculate the Surface Area of a Cube: Express Your Answer in Terms of X

Q: Why is the formula 6X² and not X³?

Surface area is 2D, volume is 3D! We're finding the total area of all 6 faces, each with area $ X^2 $. Volume uses $ X^3 $, but surface area uses $ X^2 $.

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

Think of a dice! Count them: top, bottom, front, back, left side, right side = 6 faces total. Each face is a square with the same area.

Q: What if the problem asks for volume instead?

For volume, use $ V = X^3 $ (length × width × height). For surface area, always use $ SA = 6X^2 $ (6 faces × area per face).

Q: Can I use this formula for rectangular prisms too?

No! This formula only works for cubes where all sides are equal. For rectangular prisms, you need: $ SA = 2(lw + lh + wh) $.

Q: What units should my answer have?

Since we're finding area, your answer should be in square units. If X is in centimeters, your answer is in $ cm^2 $.

Surface Area Formulas with Variable Side Lengths

What is the surface area of the cube below in terms of X?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Express the surface area of the cube

00:03 Every cube has 6 faces

00:17 Therefore multiply the area of one face by 6 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

What is the surface area of the cube below in terms of X?

Step-by-step solution

To solve this problem, we'll determine the surface area using the formula for a cube:

Step 1: Identify the given information — Each side of the cube is $X$ .
Step 2: Recall the surface area formula — For a cube, it is $6 \times (\text{side length})^2$ .
Step 3: Substitute the side length $X$ into the formula.

Now, let's proceed with the solution:
Step 1: The cube has each side $= X$ .
Step 2: The surface area formula for a cube is given by $6 \times (\text{side length})^2$ .
Step 3: Substituting $X$ for the side length, we find the surface area is $6 \times X^2$ .

Therefore, the surface area of the cube in terms of $X$ is $\mathbf{6X^2}$ .

Final Answer

$6x^2$

Key Points to Remember

Essential concepts to master this topic

Formula: Cube surface area equals 6 times side squared
Technique: Substitute X for side length: $6 \times X^2 = 6X^2$
Check: Count all 6 faces each with area $X^2$ ✓

Common Mistakes

Avoid these frequent errors

Forgetting to account for all six faces
Don't calculate just $X^2$ for one face = missing 5 faces! This gives you the area of only one face, not the total surface area. Always multiply by 6 because a cube has exactly 6 equal square 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 is the formula 6X² and not X³?

Surface area is 2D, volume is 3D! We're finding the total area of all 6 faces, each with area $X^2$ . Volume uses $X^3$ , but surface area uses $X^2$ .

How do I remember that a cube has 6 faces?

Think of a dice! Count them: top, bottom, front, back, left side, right side = 6 faces total. Each face is a square with the same area.

What if the problem asks for volume instead?

For volume, use $V = X^3$ (length × width × height). For surface area, always use $SA = 6X^2$ (6 faces × area per face).

Can I use this formula for rectangular prisms too?

No! This formula only works for cubes where all sides are equal. For rectangular prisms, you need: $SA = 2(lw + lh + wh)$ .

What units should my answer have?

Since we're finding area, your answer should be in square units. If X is in centimeters, your answer is in $cm^2$ .

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