Calculate Cube Edge Length: Given Volume of 8 Cubic Centimeters

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

Square root is used for areas (2D) like $ \sqrt{16} = 4 $, while cube root is used for volumes (3D) like $ \sqrt[3]{8} = 2 $. Remember: cubes have three dimensions!

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

Look for perfect cubes! Common ones are: $ 1^3 = 1 $, $ 2^3 = 8 $, $ 3^3 = 27 $, $ 4^3 = 64 $, $ 5^3 = 125 $. Since 8 is a perfect cube, $ \sqrt[3]{8} = 2 $.

Q: Why does the cube root of 8 equal 2?

Because $ 2 \times 2 \times 2 = 8 $! The cube root asks: "What number multiplied by itself three times gives 8?" That number is 2.

Q: Can I use this method for any cube volume?

Yes! The formula $ a = \sqrt[3]{V} $ works for any cube volume. Just remember to include the correct units (like cm) in your final answer.

Volume Calculations with Cube Root

The cube below has a volume of 8 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

00:06 Let's find the edge length of the cube.

00:09 We'll use the formula for cube volume, which is edge length to the power of three.

00:15 Next, we'll plug in the given values and solve for edge A. Let's do it step by step.

00:29 And that's how we find the solution to the problem.

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

The cube below has a volume of 8 cm3.

How long is the edge of the cube?

Step-by-step solution

To find the length of an edge of the cube given its volume, we'll proceed with the following steps:

Step 1: Identify the volume of the cube.
Step 2: Use the formula for the volume of a cube to find the edge length.
Step 3: Calculate the cube root of the volume.

Step 1: The volume of the cube is given as $8$ cm $^3$ .

Step 2: We use the formula for the volume of a cube:
$V = a^3$ ,
where $V$ is the volume and $a$ is the length of the edge.

Step 3: To find the edge length $a$ , we need to take the cube root of the volume:
$a = \sqrt[3]{V} = \sqrt[3]{8}$

Calculating the cube root, we find:
$a = 2$

Therefore, the length of the edge of the cube is $2$ cm.

Final Answer

$2$ cm

Key Points to Remember

Essential concepts to master this topic

Volume Formula: For a cube, $V = a^3$ where a is edge length
Inverse Operation: Take cube root of volume: $a = \sqrt[3]{8} = 2$
Verification: Check by cubing answer: $2^3 = 2 \times 2 \times 2 = 8$ cm³ ✓

Common Mistakes

Avoid these frequent errors

Taking square root instead of cube root
Don't take the square root of 8 to get 2.83! This confuses area formulas with volume formulas and gives incorrect edge lengths. Always use cube root for volume problems because volume involves three dimensions.

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 is used for areas (2D) like $\sqrt{16} = 4$ , while cube root is used for volumes (3D) like $\sqrt[3]{8} = 2$ . Remember: cubes have three dimensions!

How do I calculate cube root without a calculator?

Look for perfect cubes! Common ones are: $1^3 = 1$ , $2^3 = 8$ , $3^3 = 27$ , $4^3 = 64$ , $5^3 = 125$ . Since 8 is a perfect cube, $\sqrt[3]{8} = 2$ .

Why does the cube root of 8 equal 2?

Because $2 \times 2 \times 2 = 8$ ! The cube root asks: "What number multiplied by itself three times gives 8?" That number is 2.

Can I use this method for any cube volume?

Yes! The formula $a = \sqrt[3]{V}$ works for any cube volume. Just remember to include the correct units (like cm) in your final answer.

What if the volume isn't a perfect cube?

You'll need a calculator to find the cube root. For example, if $V = 10$ cm³, then $a = \sqrt[3]{10} \approx 2.15$ cm. Always round appropriately based on the problem's context.

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