Calculate Cube Edge Length: Finding Sides When Volume = 1000 cm³

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

Cube root asks "what number multiplied by itself 3 times gives this result?" while square root uses 2 times. For volume problems with cubes, always use cube root: $ \sqrt[3]{1000} = 10 $.

Q: How do I calculate cube roots without a calculator?

Look for perfect cubes you know! $ 1^3 = 1 $, $ 2^3 = 8 $, $ 3^3 = 27 $, $ 4^3 = 64 $, $ 5^3 = 125 $, $ 10^3 = 1000 $. Memorizing these helps you recognize patterns!

Q: Why is 1000 considered a perfect cube?

Because $ 10 \times 10 \times 10 = 1000 $ exactly! Perfect cubes are numbers that result from multiplying a whole number by itself three times. This makes the cube root calculation easy.

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

You'd still use the same method: $ a = \sqrt[3]{V} $. The answer might be a decimal instead of a whole number, but the process stays the same. Always round appropriately for real-world measurements.

Q: Can I use this method for rectangular boxes?

No! This only works for cubes where all edges are equal. For rectangular boxes, you need length × width × height = volume, which requires different solving methods since you have three different measurements.

Q: How do I check if my cube root is correct?

Cube your answer! If $ a = 10 $, then $ 10^3 = 10 \times 10 \times 10 = 1000 $. If this equals the original volume, your answer is correct!

Cube Root Operations with Perfect Cubes

A cube has a volume
equal to 1000 cm3.

How long are the cube's edges?

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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

00:32 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

A cube has a volume
equal to 1000 cm3.

How long are the cube's edges?

Step-by-step solution

To solve the problem, follow these steps:

Step 1: Identify the given volume of the cube, $V = 1000$ cm³.
Step 2: Use the formula for the volume of a cube, $V = a^3$ , to set up the equation $a^3 = 1000$ .
Step 3: Solve for $a$ by taking the cube root of 1000, i.e., $a = \sqrt[3]{1000}$ .

Let's compute the cube root:

$a = \sqrt[3]{1000} = 10$ .

Therefore, the length of each edge of the cube is $10$ cm.

Final Answer

$10$ cm

Key Points to Remember

Essential concepts to master this topic

Formula: Volume of cube equals edge length cubed: $V = a^3$
Technique: Find cube root of volume: $\sqrt[3]{1000} = 10$ cm
Check: Verify by cubing answer: $10^3 = 10 \times 10 \times 10 = 1000$ ✓

Common Mistakes

Avoid these frequent errors

Confusing cube root with square root
Don't take the square root of 1000 and get approximately 31.6 cm! This gives an impossible edge length because you need the cube root, not square root. Always remember that for cube volume, you need the cube root to find the edge length.

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

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

Cube root asks "what number multiplied by itself 3 times gives this result?" while square root uses 2 times. For volume problems with cubes, always use cube root: $\sqrt[3]{1000} = 10$ .

How do I calculate cube roots without a calculator?

Look for perfect cubes you know! $1^3 = 1$ , $2^3 = 8$ , $3^3 = 27$ , $4^3 = 64$ , $5^3 = 125$ , $10^3 = 1000$ . Memorizing these helps you recognize patterns!

Why is 1000 considered a perfect cube?

Because $10 \times 10 \times 10 = 1000$ exactly! Perfect cubes are numbers that result from multiplying a whole number by itself three times. This makes the cube root calculation easy.

What if the volume wasn't a perfect cube?

You'd still use the same method: $a = \sqrt[3]{V}$ . The answer might be a decimal instead of a whole number, but the process stays the same. Always round appropriately for real-world measurements.

Can I use this method for rectangular boxes?

No! This only works for cubes where all edges are equal. For rectangular boxes, you need length × width × height = volume, which requires different solving methods since you have three different measurements.

How do I check if my cube root is correct?

Cube your answer! If $a = 10$ , then $10^3 = 10 \times 10 \times 10 = 1000$ . If this equals the original volume, your answer is correct!

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