Calculate Cube Side Length: Finding Edge Length for 27 cm³ Volume

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

Square root undoes squaring (x²), while cube root undoes cubing (x³). Since volume involves three dimensions, we need cube root to find the side length.

Q: How do I know if 27 is a perfect cube?

Try small numbers: $ 1^3 = 1 $, $ 2^3 = 8 $, $ 3^3 = 27 $. Since 3³ = 27 exactly, 27 is a perfect cube and its cube root is 3.

Q: What if the volume wasn't a perfect cube?

You'd still use the cube root, but the answer would be a decimal. For example, $ \sqrt[3]{30} \approx 3.11 $ cm. Use a calculator for non-perfect cubes.

Q: Can I check my answer without calculating 3³?

Yes! Since you found side length = 3 cm, think: 3 × 3 × 3. Count: 3 × 3 = 9, then 9 × 3 = 27 cm³. This matches the given volume!

Q: Why does the cube formula work for any cube?

All sides of a cube are equal length. So volume = length × width × height becomes a × a × a = a³. This is why we use cube root to reverse the process.

Cube Root Calculations with Perfect Cubes

How long are the sides of a cube that has a volume of 27 cm³?

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Step-by-step video solution

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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 the appropriate values and solve for edge A

00:26 We'll break down 27 into 3 cubed

00:33 We'll reduce what we can

00:37 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

How long are the sides of a cube that has a volume of 27 cm³?

Step-by-step solution

To solve for the side length of a cube with a volume of 27 cm³, we will apply the formula for the volume of a cube:

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

$V = a^3$

where $V$ is the volume, and $a$ is the length of each side.

Given $V = 27$ cm³, we can solve for $a$ by taking the cube root of the volume:

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

Substituting the given volume, we have:

$a = \sqrt[3]{27}$

Calculating the cube root, we find:

$a = 3$

Thus, the length of each side of the cube is $3$ cm.

Final Answer

$3$

Key Points to Remember

Essential concepts to master this topic

Volume Formula: For any cube, V = a³ where a is side length
Technique: Find cube root: $\sqrt[3]{27} = 3$ because $3^3 = 27$
Check: Verify by cubing: $3^3 = 3 \times 3 \times 3 = 27$ cm³ ✓

Common Mistakes

Avoid these frequent errors

Using square root instead of cube root
Don't find $\sqrt{27} \approx 5.2$ = wrong answer! Volume uses all three dimensions (length × width × height), so you need the cube root. Always use $\sqrt[3]{V}$ to find cube side length.

Practice Quiz

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Find a,b

FAQ

Everything you need to know about this question

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

Square root undoes squaring (x²), while cube root undoes cubing (x³). Since volume involves three dimensions, we need cube root to find the side length.

How do I know if 27 is a perfect cube?

Try small numbers: $1^3 = 1$ , $2^3 = 8$ , $3^3 = 27$ . Since 3³ = 27 exactly, 27 is a perfect cube and its cube root is 3.

What if the volume wasn't a perfect cube?

You'd still use the cube root, but the answer would be a decimal. For example, $\sqrt[3]{30} \approx 3.11$ cm. Use a calculator for non-perfect cubes.

Can I check my answer without calculating 3³?

Yes! Since you found side length = 3 cm, think: 3 × 3 × 3. Count: 3 × 3 = 9, then 9 × 3 = 27 cm³. This matches the given volume!

Why does the cube formula work for any cube?

All sides of a cube are equal length. So volume = length × width × height becomes a × a × a = a³. This is why we use cube root to reverse the process.

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