Calculate Surface Area: 10 cm Cube with Equal Edges

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

A cube has 6 faces - top, bottom, front, back, left side, and right side. Each face has the same area, so we calculate one face area $ (s^2) $ 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 $ 6s^2 $, volume uses $ s^3 $.

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

No! This $ 6s^2 $ formula only works for cubes where all edges are equal. For rectangular boxes, you need the formula $ 2(lw + lh + wh) $.

Q: How do I remember which unit to use for the answer?

Surface area is always in square units (like cm², m², ft²). Since we're multiplying length × length, we get area units. Don't forget the ² symbol!

Surface Area Calculations with Cubic Solids

A cube has edges measuring 10 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 The edge length according to the given data

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

00:11 6 times the edge squared

00:15 We'll substitute the edge length and solve for the surface area

00:19 Solve 10 squared

00:23 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 10 cm.

Calculate the surface area of the cube.

Step-by-step solution

To solve this problem, we will follow these steps:

Step 1: Identify the given information and formula to use.
Step 2: Calculate the surface area using the formula.
Step 3: Perform the arithmetic to find the answer.

Now, let's work through each step:

Step 1: We are given that the edge length of the cube is $10$ cm. The formula for the surface area of a cube is $6 \times s^2$ , where $s$ is the edge length.

Step 2: Substitute the edge length into the surface area formula:

$6 \times (10)^2$

Step 3: Calculate the surface area:

$6 \times 100 = 600$

Therefore, the total surface area of the cube is $600$ cm².

Final Answer

$600$ cm².

Key Points to Remember

Essential concepts to master this topic

Formula: Surface area of cube equals $6 \times s^2$ where s is edge length
Technique: Calculate $6 \times 10^2 = 6 \times 100 = 600$ cm²
Check: Count all 6 faces: each face is $10 \times 10 = 100$ cm², total $6 \times 100 = 600$ cm² ✓

Common Mistakes

Avoid these frequent errors

Calculating area of only one face instead of all six faces
Don't just calculate $10 \times 10 = 100$ cm² and stop = this gives only one face area! A cube has 6 identical faces, so you're missing 5 faces worth of surface area. 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 faces - top, bottom, front, back, left side, and right side. Each face has the same area, so we calculate one face area $(s^2)$ 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 $6s^2$ , volume uses $s^3$ .

Can I use this formula for rectangular boxes too?

No! This $6s^2$ formula only works for cubes where all edges are equal. For rectangular boxes, you need the formula $2(lw + lh + wh)$ .

How do I remember which unit to use for the answer?

Surface area is always in square units (like cm², m², ft²). Since we're multiplying length × length, we get area units. Don't forget the ² symbol!

What if the edge length isn't a whole number?

The same formula works! Just be extra careful with your arithmetic. For example, if edge = 2.5 cm, then surface area = $6 \times (2.5)^2 = 6 \times 6.25 = 37.5$ cm².

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