Calculate Surface Area: Cube with 3 cm Edges

Q: Why do we multiply by 6 instead of adding up each face?

Since all faces of a cube are identical squares, multiplying by 6 is faster than adding six times! It's the same result: $ 9 + 9 + 9 + 9 + 9 + 9 = 6 \times 9 = 54 $ cm².

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

Surface area measures the outside covering (like wrapping paper), while volume measures space inside. Surface area uses $ 6a^2 $, volume uses $ a^3 $.

Q: How can I visualize all 6 faces of a cube?

Think of a dice! It has a top, bottom, front, back, left side, and right side - that's 6 faces total. Each face is a square with the same area.

Q: Can I use this formula for other shapes?

No! The formula $ 6a^2 $ only works for cubes. Other shapes like rectangular prisms or spheres have different surface area formulas.

Surface Area Formula with Six Square Faces

A cube has edges measuring 3 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 Edge length according to the given data

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

00:10 6 times the edge squared

00:13 We'll substitute the edge length and solve for surface area

00:16 Calculate 9 squared

00:21 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 3 cm.

Calculate the surface area of the cube.

Step-by-step solution

To calculate the surface area of a cube, we use the formula:

$\text{Surface Area} = 6a^2$

where $a$ is the length of each edge of the cube.

Given $a = 3 \text{ cm}$ , we substitute this value into the formula:

$\text{Surface Area} = 6 \times (3)^2$

$= 6 \times 9$

$= 54 \text{ cm}^2$

Therefore, the surface area of the cube is $54 \text{ cm}^2$ .

This matches choice 4.

Final Answer

$54$ cm².

Key Points to Remember

Essential concepts to master this topic

Formula: Surface area of cube equals 6 times edge squared
Technique: Calculate $6 \times 3^2 = 6 \times 9 = 54$ square cm
Check: Count all 6 faces: each is $3 \times 3 = 9$ cm², total $6 \times 9 = 54$ cm² ✓

Common Mistakes

Avoid these frequent errors

Calculating area of only one face
Don't calculate just $3^2 = 9$ cm² and stop there = missing 5 other faces! A cube has 6 identical square faces, not just 1. Always multiply the area of one face by 6 to get total surface area.

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 we multiply by 6 instead of adding up each face?

Since all faces of a cube are identical squares, multiplying by 6 is faster than adding six times! It's the same result: $9 + 9 + 9 + 9 + 9 + 9 = 6 \times 9 = 54$ cm².

What's the difference between surface area and volume?

Surface area measures the outside covering (like wrapping paper), while volume measures space inside. Surface area uses $6a^2$ , volume uses $a^3$ .

How can I visualize all 6 faces of a cube?

Think of a dice! It has a top, bottom, front, back, left side, and right side - that's 6 faces total. Each face is a square with the same area.

What if the edge length has units like meters or inches?

Always keep the units! If edge = 3 meters, then surface area = $54$ square meters. The units get squared just like the numbers.

Can I use this formula for other shapes?

No! The formula $6a^2$ only works for cubes. Other shapes like rectangular prisms or spheres have different surface area formulas.

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