Calculate Face Area of Cube with 42 cm² Surface Area: Visual Geometry Problem

Q: Why does a cube have 6 faces 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, the total surface area is 6 times one face area.

Q: What's the difference between side length and face area?

Side length is the measurement of one edge (like 2.65 cm), while face area is the area of one square face (like 7 cm²). Face area equals side length squared!

Q: How do I know which face is highlighted in the diagram?

It doesn't matter which face is highlighted! In a cube, all faces have the same area, so any face you pick will have an area of 7 cm².

Q: Can I work backwards to check my answer?

Absolutely! Multiply your face area by 6: $ 7 \times 6 = 42 $ cm². If this equals the given surface area, your answer is correct!

Surface Area Formulas with Face Calculations

A cube has a surface area equal to 42 cm².

What is the area of the face highlighted below?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:08 Let's find the area of one face of a cube.

00:12 We’ll use A for edge length. Every edge in the cube is the same length.

00:17 The total surface area of the cube is six times the area of one face.

00:22 Now, let's plug in our values and solve for the area of the face.

00:27 Great! We'll focus on finding just the face area now.

00:32 And there you have it. That's the solution!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

A cube has a surface area equal to 42 cm².

What is the area of the face highlighted below?

Step-by-step solution

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

Step 1: Use the formula for the surface area of a cube: $S = 6s^2$ .
Step 2: Plug in the given total surface area into the formula to find $s^2$ .
Step 3: Calculate the area of one face of the cube.

Now, let's work through each step:
Step 1: We are given that the total surface area $S$ is 42 cm².
Step 2: Substitute the given surface area into the formula: $6s^2 = 42$
To find $s^2$ , divide both sides of the equation by 6: $s^2 = \frac{42}{6} = 7$
Step 3: The area of one face of the cube equals $s^2$ , so the area of one face is 7 cm².

Therefore, the area of the face highlighted is $7 \, \text{cm}^2$ .

Final Answer

$7$

Key Points to Remember

Essential concepts to master this topic

Formula: Surface area of cube equals 6 times one face area
Technique: Divide total surface area by 6: $s^2 = \frac{42}{6} = 7$
Check: Verify by multiplying face area by 6: $7 \times 6 = 42$ ✓

Common Mistakes

Avoid these frequent errors

Finding the side length instead of face area
Don't solve for s by taking the square root of 7 = 2.65 cm! The question asks for face area, not side length. Always read what the question is asking for - face area equals s², which is 7 cm².

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 does a cube have 6 faces 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, the total surface area is 6 times one face area.

What's the difference between side length and face area?

Side length is the measurement of one edge (like 2.65 cm), while face area is the area of one square face (like 7 cm²). Face area equals side length squared!

How do I know which face is highlighted in the diagram?

It doesn't matter which face is highlighted! In a cube, all faces have the same area, so any face you pick will have an area of 7 cm².

Can I work backwards to check my answer?

Absolutely! Multiply your face area by 6: $7 \times 6 = 42$ cm². If this equals the given surface area, your answer is correct!

What if the surface area wasn't a nice number like 42?

The same method works! Just divide the surface area by 6 to get the face area. You might get a fraction or decimal, which is perfectly fine for face area.

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