Calculate Cube Edge Length: Finding Sides of a 64 cm³ Cube

Q: What exactly is a cube root?

A cube root is the number that, when multiplied by itself three times, gives you the original number. So $ \sqrt[3]{64} = 4 $ because $ 4 \times 4 \times 4 = 64 $.

Q: How do I remember which root to use for cubes?

Think dimensions! Cubes are 3D shapes, so use the 3rd root (cube root). For squares (2D), use square root. The dimension matches the root!

Q: Can I just guess and check the answer?

Sure! Try each answer choice: $ 3^3 = 27 $, $ 4^3 = 64 $ ✓, $ 5^3 = 125 $. This method works great for multiple choice!

Q: Why do all edges of a cube have the same length?

That's what makes it a cube! By definition, a cube has all edges equal, all faces are squares, and all angles are 90°. If edges were different lengths, it would be a rectangular prism instead.

Cube Root Calculation with Perfect Cubes

Shown below is a cube with a volume of 64 cm³.

How long are the edges of the cube?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find the cube's edge

00:03 We'll use the formula for calculating cube volume (edge to the power of 3)

00:09 We'll substitute appropriate values and solve for edge A

00:24 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

Shown below is a cube with a volume of 64 cm³.

How long are the edges of the cube?

Step-by-step solution

To find the length of the edges of the cube, we will utilize the relationship between the volume and the edge length for a cube. Specifically, the volume $V$ of a cube with edge length $a$ is given by the formula:

$V = a^3$

Given that the volume of the cube is 64 cm³, we set up the equation:

$a^3 = 64$

To solve for $a$ , we need to find the cube root of 64:

$a = \sqrt[3]{64}$

Recognizing that 64 is a perfect cube, we can confirm that:

$\sqrt[3]{64} = 4$

Thus, the length of each edge of the cube is 4 cm.

This solution matches option 3, which is 4 cm, as the correct choice.

Final Answer

$4$ cm

Key Points to Remember

Essential concepts to master this topic

Cube Volume Formula: Volume equals edge length cubed: $V = a^3$
Technique: Find cube root: $\sqrt[3]{64} = 4$ since $4^3 = 64$
Check: Verify by cubing the answer: $4^3 = 4 \times 4 \times 4 = 64$ cm³ ✓

Common Mistakes

Avoid these frequent errors

Confusing cube root with square root
Don't find $\sqrt{64} = 8$ instead of $\sqrt[3]{64}$ = wrong dimension! Square root gives you area relationships, not volume. Always use cube root for three-dimensional problems like finding cube edges.

Practice Quiz

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Identify the correct 2D pattern of the given cuboid:

FAQ

Everything you need to know about this question

What exactly is a cube root?

A cube root is the number that, when multiplied by itself three times, gives you the original number. So $\sqrt[3]{64} = 4$ because $4 \times 4 \times 4 = 64$ .

How do I remember which root to use for cubes?

Think dimensions! Cubes are 3D shapes, so use the 3rd root (cube root). For squares (2D), use square root. The dimension matches the root!

What if the volume isn't a perfect cube?

You'll need a calculator to find the cube root! But in most textbook problems, volumes are perfect cubes like 8, 27, 64, or 125 to make calculations easier.

Can I just guess and check the answer?

Sure! Try each answer choice: $3^3 = 27$ , $4^3 = 64$ ✓, $5^3 = 125$ . This method works great for multiple choice!

Why do all edges of a cube have the same length?

That's what makes it a cube! By definition, a cube has all edges equal, all faces are squares, and all angles are 90°. If edges were different lengths, it would be a rectangular prism instead.

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