Calculate Cube Edge Length: Finding Side Length of a 27 cm³ Cube

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

Square root asks "what number times itself gives this?" while cube root asks "what number times itself three times gives this?" For cubes, always use cube root: $ \sqrt[3]{27} = 3 $ because $ 3 \times 3 \times 3 = 27 $.

Q: How do I find cube roots of numbers that aren't perfect cubes?

Use a calculator! For example, $ \sqrt[3]{20} \approx 2.71 $. But in math class, problems usually use perfect cubes like 1, 8, 27, 64, 125, so you can find exact answers.

Q: Why is 27 called a 'perfect cube'?

A perfect cube is a whole number that equals another whole number cubed. Since $ 3^3 = 27 $, we say 27 is a perfect cube. Other examples: $ 2^3 = 8 $, $ 4^3 = 64 $, $ 5^3 = 125 $.

Q: Can I just divide 27 by 3 to get the edge length?

No! That would give you 9, which is wrong. Division works for area problems, but cubes involve three dimensions. You must use the cube root operation to reverse the cubing process.

Q: How can I remember the first few perfect cubes?

Practice these key ones: $ 1^3 = 1 $, $ 2^3 = 8 $, $ 3^3 = 27 $, $ 4^3 = 64 $, $ 5^3 = 125 $. Try making flash cards or saying them out loud!

Cube Root Operations with Perfect Cubes

The cube has a volume equal to 27 cm3.

Calculate the length of the cube's edges.

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Step-by-step video solution

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00:00 Find the cube's edge

00:03 We'll use the formula for calculating cube volume (edge cubed)

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

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Understand the problem

The cube has a volume equal to 27 cm3.

Calculate the length of the cube's edges.

Step-by-step solution

To solve the problem of finding the length of the cube's edges, we begin with the formula for the volume of a cube, which is:

$V = a^3$

where $V$ is the volume and $a$ is the length of one edge of the cube.

Given that the volume $V$ is 27 cm $^3$ , we can substitute it into the formula:

$27 = a^3$

To solve for $a$ , we need to take the cube root of both sides of the equation:

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

Since 27 is a perfect cube (as $27 = 3^3$ ), the cube root of 27 is 3. Thus,

$a = 3$ cm

Therefore, the length of each edge of the cube is $\mathbf{3}$ cm.

Final Answer

$3$ cm

Key Points to Remember

Essential concepts to master this topic

Volume Formula: For a cube, volume equals side length cubed: $V = a^3$
Inverse Operation: To find edge length, take cube root: $a = \sqrt[3]{27} = 3$
Verification: Check by cubing your answer: $3^3 = 3 \times 3 \times 3 = 27$ ✓

Common Mistakes

Avoid these frequent errors

Confusing square roots with cube roots
Don't use $\sqrt{27} \approx 5.2$ = wrong answer! Square roots are for area problems, not volume. Always use cube roots $\sqrt[3]{27} = 3$ for finding cube edge lengths.

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's the difference between square root and cube root?

Square root asks "what number times itself gives this?" while cube root asks "what number times itself three times gives this?" For cubes, always use cube root: $\sqrt[3]{27} = 3$ because $3 \times 3 \times 3 = 27$ .

How do I find cube roots of numbers that aren't perfect cubes?

Use a calculator! For example, $\sqrt[3]{20} \approx 2.71$ . But in math class, problems usually use perfect cubes like 1, 8, 27, 64, 125, so you can find exact answers.

Why is 27 called a 'perfect cube'?

A perfect cube is a whole number that equals another whole number cubed. Since $3^3 = 27$ , we say 27 is a perfect cube. Other examples: $2^3 = 8$ , $4^3 = 64$ , $5^3 = 125$ .

Can I just divide 27 by 3 to get the edge length?

No! That would give you 9, which is wrong. Division works for area problems, but cubes involve three dimensions. You must use the cube root operation to reverse the cubing process.

How can I remember the first few perfect cubes?

Practice these key ones: $1^3 = 1$ , $2^3 = 8$ , $3^3 = 27$ , $4^3 = 64$ , $5^3 = 125$ . Try making flash cards or saying them out loud!

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