Calculate Surface Area of a Cube with 5 cm Edges: Geometric Problem

Q: Why do we multiply by 6 instead of adding the areas?

A cube has 6 identical square faces (top, bottom, front, back, left, right). Since all faces are the same size, multiplying by 6 is much faster than adding $25 + 25 + 25 + 25 + 25 + 25$!

Q: What if I accidentally use the perimeter formula?

The perimeter of one face would be $4 \times 5 = 20$ cm, which is much smaller than our answer of 150 cm². Remember: surface area uses $a^2$ (squared), while perimeter uses $4a$ (not squared).

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

Think of a dice or box! You can see the top, front, and right side faces. The hidden faces are the bottom, back, and left side. Each face is a perfect square with area $5 \times 5 = 25$ cm².

Q: Is there a shortcut to check my answer?

Yes! A cube's surface area should always be 6 times larger than one face's area. Since one face = 25 cm², the total should be around $6 \times 25 = 150$ cm².

Q: What units should my final answer have?

Since we're calculating area, the units are always squared. Edge length is in cm, so surface area is in cm² (square centimeters). Never forget the ² symbol!

Surface Area Calculation with Cube Geometry

A cube has edges measuring 5 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 Let's substitute the edge length and solve for the surface area

00:16 Let's substitute the edge length and solve for the surface area

00:19 Calculate 5 squared

00:24 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 5 cm.

Calculate the surface area of the cube.

Step-by-step solution

To determine the surface area of the cube, we will follow a systematic approach:

Step 1: Identify the provided information.
The edge length of the cube is given as $5$ cm.
Step 2: Utilize the formula for the surface area of a cube.
The formula is $6a^2$ , with $a$ representing the edge length of the cube.
Step 3: Substitute the given edge length into the formula and perform the calculation.
Using $a = 5$ cm, the calculation becomes:
$6 \times (5 \, \text{cm})^2 = 6 \times 25 \, \text{cm}^2 = 150 \, \text{cm}^2.$

The computed surface area of the cube is therefore $150$ cm².

Therefore, the correct choice among the given options is the fourth choice, which is $150 ~cm²$ .

Final Answer

$150$ cm².

Key Points to Remember

Essential concepts to master this topic

Formula: A cube has 6 identical square faces, so use $6a^2$
Technique: Square the edge first: $5^2 = 25$ , then multiply by 6
Check: Each face is $25$ cm², and $6 \times 25 = 150$ cm² ✓

Common Mistakes

Avoid these frequent errors

Calculating area of only one face
Don't calculate just $5^2 = 25$ cm² and stop! This gives the area of one face, not the total surface. A cube has 6 faces that need paint or covering. Always multiply the face area by 6 to get the complete 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 the areas?

A cube has 6 identical square faces (top, bottom, front, back, left, right). Since all faces are the same size, multiplying by 6 is much faster than adding $25 + 25 + 25 + 25 + 25 + 25$ !

What if I accidentally use the perimeter formula?

The perimeter of one face would be $4 \times 5 = 20$ cm, which is much smaller than our answer of 150 cm². Remember: surface area uses $a^2$ (squared), while perimeter uses $4a$ (not squared).

How can I visualize all 6 faces of a cube?

Think of a dice or box! You can see the top, front, and right side faces. The hidden faces are the bottom, back, and left side. Each face is a perfect square with area $5 \times 5 = 25$ cm².

Is there a shortcut to check my answer?

Yes! A cube's surface area should always be 6 times larger than one face's area. Since one face = 25 cm², the total should be around $6 \times 25 = 150$ cm².

What units should my final answer have?

Since we're calculating area, the units are always squared. Edge length is in cm, so surface area is in cm² (square centimeters). Never forget the ² symbol!

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