Calculate the Volume of a Cube with 3 cm Edges: Step-by-Step Solution

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

A cube is three-dimensional, so you need length × width × height. Since all edges are equal (3 cm), you multiply 3 × 3 × 3, which equals $ 3^3 = 27 $ cm³.

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

cm² measures area (flat surfaces), while cm³ measures volume (3D space). Since we're finding how much space the cube takes up, we use cm³.

Q: How do I remember the cube volume formula?

Think of it as "side times side times side" because a cube has three equal dimensions. The formula $ V = s^3 $ just shortens this multiplication!

Q: What if the edge was 4 cm instead of 3 cm?

You'd calculate $ 4^3 = 4 \times 4 \times 4 = 64 $ cm³. The method stays the same - just cube whatever the edge length is!

Q: Can I check my answer without redoing the whole calculation?

Yes! Ask yourself: "Does 27 make sense?" Since $ 3^3 $ should be bigger than $ 3^2 = 9 $ but not huge, 27 cm³ is reasonable for a small cube.

Cube Volume with Edge Measurements

A cube has edges measuring 3 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

00:00 Calculate the volume of the cube

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

00:07 Edge length according to the given data

00:12 We'll substitute the edge length and solve for the volume

00:20 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 edges measuring 3 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 appropriate formula for volume.
Step 3: Perform the necessary calculations.

Now, let's work through each step:
Step 1: The problem states that each edge of the cube is 3 cm long.
Step 2: We use the formula for the volume of a cube: $V = s^3$ , where $s$ is the side length.
Step 3: Substituting the side length into the formula gives us $V = 3^3$ . Calculating this, we have:

$3^3 = 3 \times 3 \times 3 = 27$ .

Therefore, the volume of the cube is $27$ cm³.

Given the answer choices, the correct choice is $\textbf{27 cm³}$ .

Final Answer

$27$ cm³

Key Points to Remember

Essential concepts to master this topic

Formula: Volume of a cube equals side length cubed: $V = s^3$
Technique: Substitute edge length: $V = 3^3 = 3 \times 3 \times 3 = 27$
Check: Verify units are cubic: edge in cm gives volume in cm³ ✓

Common Mistakes

Avoid these frequent errors

Using wrong formula or calculation
Don't calculate $3 \times 6 = 18$ or $3^2 = 9$ = wrong volume! This confuses cube volume with surface area or square area formulas. Always use $V = s^3$ and multiply the edge length 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 I cube the edge length instead of just multiplying by 3?

A cube is three-dimensional, so you need length × width × height. Since all edges are equal (3 cm), you multiply 3 × 3 × 3, which equals $3^3 = 27$ cm³.

What's the difference between cm² and cm³?

cm² measures area (flat surfaces), while cm³ measures volume (3D space). Since we're finding how much space the cube takes up, we use cm³.

How do I remember the cube volume formula?

Think of it as "side times side times side" because a cube has three equal dimensions. The formula $V = s^3$ just shortens this multiplication!

What if the edge was 4 cm instead of 3 cm?

You'd calculate $4^3 = 4 \times 4 \times 4 = 64$ cm³. The method stays the same - just cube whatever the edge length is!

Can I check my answer without redoing the whole calculation?

Yes! Ask yourself: "Does 27 make sense?" Since $3^3$ should be bigger than $3^2 = 9$ but not huge, 27 cm³ is reasonable for a small cube.

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