Calculate Cube Volume: Finding V When Edge Length = 10 cm

Q: Why do we cube the side length instead of squaring it?

A cube has three dimensions: length, width, and height. We multiply all three together: 10 × 10 × 10 = $ 10^3 $. Squaring only gives you area (flat surface), not volume (3D space)!

Q: What does cm³ mean exactly?

cm³ means cubic centimeters - it's the unit for volume. Think of it as counting tiny 1 cm × 1 cm × 1 cm cubes that fit inside your larger cube. That's why we get 1000 of them!

Q: Is there an easier way to remember the cube volume formula?

Think "side × side × side" or remember that cubes have equal edges, so you're multiplying the same number three times: $ s × s × s = s^3 $.

Q: What if the edge length was a decimal like 2.5 cm?

Same formula! $ V = 2.5^3 = 2.5 × 2.5 × 2.5 = 15.625 $ cm³. Just be careful with your decimal multiplication and keep track of decimal places.

Volume Formula with Cubic Power

A cube has edges measuring 10 cm long.

Calculate the volume of the cube.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Calculate the volume of the cube

00:03 The edge length according to the given data

00:07 We'll use the formula for calculating cube volume (edge cubed):

00:11 We'll substitute the edge length and solve for the volume

00:15 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

A cube has edges measuring 10 cm long.

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 appropriate formula for calculating the volume of a cube.
Step 3: Perform the necessary calculation to find the volume.

Let's work through each step:
Step 1: We know the length of each edge of the cube is 10 cm.
Step 2: The formula for the volume $V$ of a cube with side length $s$ is given by $V = s^3$ .
Step 3: Plugging the given side length into the formula, we get:
$V = 10^3 = 1000$ cm³.

Therefore, the volume of the cube is $1000$ cm³.

Final Answer

$1000$ cm³

Key Points to Remember

Essential concepts to master this topic

Formula: Volume of cube equals side length cubed: $V = s^3$
Calculation: For 10 cm edges: $V = 10^3 = 1000$ cm³
Check: Units must be cubic (cm³) and result makes sense for given dimensions ✓

Common Mistakes

Avoid these frequent errors

Using wrong formula or calculating incorrectly
Don't multiply 10 × 3 = 30 cm³ or use $V = s^2$ = 100 cm³! These give flat area formulas, not volume. Always use $V = s^3$ and calculate 10 × 10 × 10 for three-dimensional space.

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

Why do we cube the side length instead of squaring it?

A cube has three dimensions: length, width, and height. We multiply all three together: 10 × 10 × 10 = $10^3$ . Squaring only gives you area (flat surface), not volume (3D space)!

What does cm³ mean exactly?

cm³ means cubic centimeters - it's the unit for volume. Think of it as counting tiny 1 cm × 1 cm × 1 cm cubes that fit inside your larger cube. That's why we get 1000 of them!

Is there an easier way to remember the cube volume formula?

Think "side × side × side" or remember that cubes have equal edges, so you're multiplying the same number three times: $s × s × s = s^3$ .

How can I check if 1000 cm³ is reasonable?

A 10 cm cube is about the size of a large orange. 1000 cm³ = 1 liter, which sounds right for that size! If you got 30 or 100, that would be way too small.

What if the edge length was a decimal like 2.5 cm?

Same formula! $V = 2.5^3 = 2.5 × 2.5 × 2.5 = 15.625$ cm³. Just be careful with your decimal multiplication and keep track of decimal places.

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