Calculate Cube Side Length from Surface Area: 24 cm² Problem

Q: Why does a cube have 6 faces in the formula?

A cube has 6 identical square faces: top, bottom, front, back, left, and right. Since each face has area $ a^2 $, the total surface area is $ 6a^2 $.

Q: How is this different from finding the volume of a cube?

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

Q: Can I work backwards to check my answer?

Absolutely! Take your side length and calculate: $ 6 \times (2)^2 = 6 \times 4 = 24 \text{ cm}^2 $. If you get the original surface area, you're correct!

Q: What units should my final answer have?

Since we started with surface area in cm², the side length will be in cm (not cm²). Surface area is squared units, length is single units.

Surface Area Formulas with Square Root Solutions

The surface area of a cube is 24 cm².

How long are the sides of the cube?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:06 Let's figure out the length of a cube's edge.

00:10 Remember, a cube's edges are all the same.

00:15 A cube has six faces, so the surface area is six times the area of one face.

00:31 Now, we'll plug in the numbers and solve for edge length, A.

00:35 Let's focus on finding the value of A.

00:51 And that's how we find the cube's edge length!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

The surface area of a cube is 24 cm².

How long are the sides of the cube?

Step-by-step solution

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

Step 1: Identify the known information.
Step 2: Apply the surface area formula for the cube.
Step 3: Solve for the side length of the cube.

Now, let's work through each step:

Step 1: We know the total surface area of the cube is given as 24 cm².

Step 2: The formula for the surface area of a cube is:

$S = 6a^2$

where $S$ is the surface area and $a$ is the side length of the cube.

Step 3: We set the surface area equal to 24 cm² and solve for $a$ :

$6a^2 = 24$

Divide both sides by 6:

$a^2 = 4$

Take the square root of both sides to solve for $a$ :

$a = \sqrt{4} = 2 \text{ cm}$

Therefore, the length of each side of the cube is $2 \, \text{cm}$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Formula: Surface area of cube equals 6 times side squared
Technique: Set $6a^2 = 24$ then divide by 6 to get $a^2 = 4$
Check: Verify $6(2)^2 = 6 \times 4 = 24 \text{ cm}^2$ ✓

Common Mistakes

Avoid these frequent errors

Forgetting to take the square root after finding a²
Don't stop at a² = 4 thinking the answer is 4 cm = wrong side length! This gives you the area of one face, not the side length. Always take the square root: √4 = 2 cm to find the actual side length.

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 does a cube have 6 faces in the formula?

A cube has 6 identical square faces: top, bottom, front, back, left, and right. Since each face has area $a^2$ , the total surface area is $6a^2$ .

What if I get a decimal when taking the square root?

Sometimes the square root won't be a whole number! Use a calculator and round appropriately based on the problem's context. Always check if your answer makes sense.

How is this different from finding the volume of a cube?

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

Can I work backwards to check my answer?

Absolutely! Take your side length and calculate: $6 \times (2)^2 = 6 \times 4 = 24 \text{ cm}^2$ . If you get the original surface area, you're correct!

What units should my final answer have?

Since we started with surface area in cm², the side length will be in cm (not cm²). Surface area is squared units, length is single units.

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