Calculate Cube Edge Length from Volume: Finding Side Length of 216 cm³ Cube

Q: How do I find the cube root of 216 without a calculator?

Try testing small numbers: 5³ = 125 (too small), 6³ = 216 (perfect!), 7³ = 343 (too big). Practice memorizing perfect cubes: 1³=1, 2³=8, 3³=27, 4³=64, 5³=125, 6³=216.

Q: Why is it cube root and not square root?

Because a cube has three dimensions! Volume = length × width × height, and since all sides are equal in a cube, we need to "undo" the cubing operation with a cube root.

Q: What's the difference between ³√ and √?

The small 3 means cube root (what number times itself 3 times gives this result), while regular √ means square root (what number times itself 2 times gives this result).

Cube Root Calculations with Perfect Cubes

A cube has a volume of 216 cm3

How long is 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

00:04 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

00:25 And this is the solution to the problem

Step-by-step written solution

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Understand the problem

A cube has a volume of 216 cm3

How long is the edge of the cube?

Step-by-step solution

To find the length of the edge of a cube with a volume of 216 cm $^3$ , we need to find the cube root of 216.

The formula for the volume of a cube is given by:

$\text{Volume} = s^3$ , where $s$ is the length of an edge of the cube.

We are given the volume $216 \, \text{cm}^3$ , so we set up the equation:

$s^3 = 216$

To solve for $s$ , we take the cube root of both sides of the equation:

$s = \sqrt[3]{216}$

Calculating the cube root of 216, we find:

$\sqrt[3]{216} = 6$

Therefore, the length of each edge of the cube is $6$ cm.

The correct answer to the problem is $6$ cm.

Final Answer

$6$ cm

Key Points to Remember

Essential concepts to master this topic

Volume Formula: Volume equals side length cubed ( $V = s^3$ )
Cube Root Method: Find $s = \sqrt[3]{216} = 6$ by reverse calculation
Verification: Check that $6^3 = 6 \times 6 \times 6 = 216$ ✓

Common Mistakes

Avoid these frequent errors

Using square root instead of cube root
Don't find $\sqrt{216} \approx 14.7$ = wrong answer! This treats it like finding the side of a square, not a cube. Always use the cube root $\sqrt[3]{216} = 6$ 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 216 without a calculator?

Try testing small numbers: 5³ = 125 (too small), 6³ = 216 (perfect!), 7³ = 343 (too big). Practice memorizing perfect cubes: 1³=1, 2³=8, 3³=27, 4³=64, 5³=125, 6³=216.

What if the volume isn't a perfect cube?

Use a calculator to find the cube root, or estimate between two perfect cubes. For example, if volume is 250, the edge length is between 6 and 7 cm since 6³=216 and 7³=343.

Why is it cube root and not square root?

Because a cube has three dimensions! Volume = length × width × height, and since all sides are equal in a cube, we need to "undo" the cubing operation with a cube root.

How can I check if my answer is correct?

Multiply your answer by itself three times. If you get 6 cm, check: 6 × 6 × 6 = 216 cm³. If it matches the original volume, you're right!

What's the difference between ³√ and √?

The small 3 means cube root (what number times itself 3 times gives this result), while regular √ means square root (what number times itself 2 times gives this result).

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