Calculate the Surface Area of a Cube with 9 cm Edges: Geometric Problem

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. Each face has 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 area and surface area?

Area measures one flat surface (like one face of the cube = 81 cm²). Surface area measures all the outside surfaces combined (all 6 faces = 486 cm²).

Q: Can I use this formula for any cube?

Yes! The formula $ A = 6s^2 $ works for any cube, no matter what size. Just substitute your edge length for 's' and follow the same steps.

Q: How do I remember that cubes have 6 faces?

Think of a dice or building block! You can see the top, and if you pick it up and turn it around, you'll count exactly 6 square faces total.

Surface Area Calculations with Cube Geometry

A cube has edges measuring 9 cm long.

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

00:09 6 times the edge squared

00:13 Let's substitute the edge length and solve for surface area

00:20 Let's solve 9 squared

00:26 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 9 cm long.

Calculate the surface area of the cube.

Step-by-step solution

To solve this problem, we will calculate the surface area of a cube with each edge measuring 9 cm using the formula for the surface area of a cube.

Step 1: Identify the given information
The edge length $s$ of the cube is 9 cm.

Step 2: Apply the formula for the surface area
The formula for the surface area $A$ of a cube is $A = 6s^2$ .

Step 3: Perform the calculation
Plug the given value into the formula:

$A = 6 \times (9 \, \text{cm})^2$

Calculate the square of the side length:
$9^2 = 81 \, \text{cm}^2$

Now multiply by 6 to find the total surface area:
$A = 6 \times 81 \, \text{cm}^2 = 486 \, \text{cm}^2$

Therefore, the surface area of the cube is $486 \, \text{cm}^2$ .

Final Answer

$486$ cm²

Key Points to Remember

Essential concepts to master this topic

Formula: Surface area of cube equals 6 times side squared
Technique: Calculate $6 \times 9^2 = 6 \times 81 = 486$ cm²
Check: Count all 6 faces: each face is 81 cm², total 486 cm² ✓

Common Mistakes

Avoid these frequent errors

Using formula for area of one face only
Don't calculate just 9² = 81 cm² and stop there! This gives only one face area, not the complete surface. A cube has 6 identical faces. Always multiply the face area by 6 to get total surface area.

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

What's the difference between area and surface area?

Area measures one flat surface (like one face of the cube = 81 cm²). Surface area measures all the outside surfaces combined (all 6 faces = 486 cm²).

Can I use this formula for any cube?

Yes! The formula $A = 6s^2$ works for any cube, no matter what size. Just substitute your edge length for 's' and follow the same steps.

How do I remember that cubes have 6 faces?

Think of a dice or building block! You can see the top, and if you pick it up and turn it around, you'll count exactly 6 square faces total.

What if I get a decimal answer?

That's perfectly normal! Many surface area problems result in decimal answers. Just make sure to include the correct units (like cm²) and round appropriately if needed.

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