Calculate the Edge Length of a Cube with Volume 512 cm³

Q: What's the difference between square root and cube root?

Square root finds the side of a square (2D), while cube root finds the edge of a cube (3D). For volume problems, always use cube root!

Q: How can I remember the cube volume formula?

Think of it as length × width × height, but since all sides are equal in a cube, it's s × s × s = s³. The edge appears three times!

Q: Why do we write the answer as 8 cm and not just 8?

Always include units in your final answer! Since volume was given in cm³, the edge length must be in cm. Units help you check if your answer makes sense.

Cube Root Calculations with Perfect Powers

The cube shown below has a volume of 512 cm3.

What is the length of the edge 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)

00:08 We'll substitute appropriate values and solve for edge A

00:25 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

The cube shown below has a volume of 512 cm3.

What is the length of the edge of the cube?

Step-by-step solution

To determine the length of one edge of a cube with a volume of 512 cm³, we follow these steps:

Step 1: Understand the relationship between volume and edge length for a cube. The volume $V$ is given by the formula $V = s^3$ , where $s$ is the edge length.
Step 2: Replace the volume in the formula with the given value: $512 = s^3$ .
Step 3: To find $s$ , take the cube root of both sides of the equation: $s = \sqrt[3]{512}$ .
Step 4: Calculate the cube root of 512. Factoring 512, we find $512 = 8 \times 8 \times 8$ , so $\sqrt[3]{512} = 8$ .

Thus, the length of each edge of the cube is $8$ cm.

Final Answer

$8$ cm

Key Points to Remember

Essential concepts to master this topic

Formula: Volume of cube equals edge length cubed: $V = s^3$
Technique: Take cube root of volume: $s = \sqrt[3]{512} = 8$
Check: Verify by cubing answer: $8^3 = 8 \times 8 \times 8 = 512$ ✓

Common Mistakes

Avoid these frequent errors

Confusing cube root with square root
Don't take the square root of 512 to get approximately 22.6 = wrong answer! Square root gives the side of a square, not a cube. Always use cube root for three-dimensional volume problems.

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

How do I find the cube root of 512 without a calculator?

Try to factor 512 into three equal parts! Start with small numbers: 8 × 8 × 8 = 512. So $\sqrt[3]{512} = 8$ . Practice with perfect cubes like 27, 64, 125!

What's the difference between square root and cube root?

Square root finds the side of a square (2D), while cube root finds the edge of a cube (3D). For volume problems, always use cube root!

What if the volume isn't a perfect cube?

Use a calculator or estimation! For example, if volume is 500, the edge length is between 7 and 8 since $7^3 = 343$ and $8^3 = 512$ .

How can I remember the cube volume formula?

Think of it as length × width × height, but since all sides are equal in a cube, it's s × s × s = s³. The edge appears three times!

Why do we write the answer as 8 cm and not just 8?

Always include units in your final answer! Since volume was given in cm³, the edge length must be in cm. Units help you check if your answer makes sense.

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