Calculate Cube Volume: Finding Volume with 8 cm Edge Length

Q: Why do we cube the edge length instead of just multiplying by 3?

Volume measures 3-dimensional space! A cube has length, width, and height all equal to the edge. So you multiply edge × edge × edge = $ s^3 $ to fill the entire 3D space.

Q: What's the difference between cm² and cm³?

cm² measures area (flat surfaces like a square), while cm³ measures volume (3D space inside shapes). Volume always uses cubic units!

Q: How can I remember that 8³ = 512?

Break it down: $ 8^2 = 64 $, then $ 64 \times 8 = 512 $. Or remember that 8 is $ 2^3 $, so $ 8^3 = (2^3)^3 = 2^9 = 512 $!

Q: Can I use a calculator for cubing numbers?

Absolutely! For larger numbers or decimals, calculators help avoid errors. Look for an x³ button or use the ^ key to enter exponents.

Volume Calculation with Perfect Cubes

The edges of a cube measure 8 cm.

Calculate the volume of the cube.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:05 Let's find the volume of the cube.

00:08 First, check the length of each edge.

00:11 To calculate, use the formula: edge length cubed.

00:16 Substitute the edge length into the formula, and solve for the volume.

00:21 And that's how we find the volume of a cube! Great job!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

The edges of a cube measure 8 cm.

Calculate the volume of the cube.

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Identify the given information
Step 2: Apply the formula for the volume of a cube
Step 3: Perform the necessary calculations to find the volume

Now, let's work through each step:
Step 1: The problem gives us the edge length of the cube as 8 cm.
Step 2: We'll use the formula for the volume of a cube, which is $V = s^3$ , where $s$ is the edge length.
Step 3: Plugging the edge length into the formula, we have $V = 8^3$ . This calculates to:
$V = 8 \times 8 \times 8 = 512$ .

Therefore, the volume of the cube is $512$ cm³, which is option 2 from the choices given.

Final Answer

$512$ cm³

Key Points to Remember

Essential concepts to master this topic

Formula: Volume of cube equals edge length cubed: $V = s^3$
Calculation: For 8 cm edge: $8^3 = 8 \times 8 \times 8 = 512$ cm³
Check: Verify by counting: 8×8×8 = 64×8 = 512 cubic units ✓

Common Mistakes

Avoid these frequent errors

Using wrong formula or confusing with surface area
Don't use $6s^2$ (surface area formula) = 384 cm²! That's the total area of all faces, not volume. Always use $V = s^3$ for volume - multiply the edge length by itself three times.

Practice Quiz

Test your knowledge with interactive questions

Identify the correct 2D pattern of the given cuboid:

FAQ

Everything you need to know about this question

Why do we cube the edge length instead of just multiplying by 3?

Volume measures 3-dimensional space! A cube has length, width, and height all equal to the edge. So you multiply edge × edge × edge = $s^3$ to fill the entire 3D space.

What's the difference between cm² and cm³?

cm² measures area (flat surfaces like a square), while cm³ measures volume (3D space inside shapes). Volume always uses cubic units!

How can I remember that 8³ = 512?

Break it down: $8^2 = 64$ , then $64 \times 8 = 512$ . Or remember that 8 is $2^3$ , so $8^3 = (2^3)^3 = 2^9 = 512$ !

What if the edge length wasn't a whole number?

The same formula works! For example, if the edge was 2.5 cm, you'd calculate $2.5^3 = 2.5 \times 2.5 \times 2.5 = 15.625$ cm³.

Can I use a calculator for cubing numbers?

Absolutely! For larger numbers or decimals, calculators help avoid errors. Look for an x³ button or use the ^ key to enter exponents.

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