Calculate Cube Volume: Finding Volume with 3 cm Edge Length

Q: Why do I cube the edge length instead of just squaring it?

Because volume measures 3-dimensional space! You need length × width × height. Since all edges are equal in a cube, that's edge × edge × edge = edge³.

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

cm² measures area (flat surfaces like a square), while cm³ measures volume (space inside a 3D shape). Always use cubic units for volume!

Q: How is 3³ different from 3 × 3?

$ 3^2 = 3 \times 3 = 9 $ (area of one face), but $ 3^3 = 3 \times 3 \times 3 = 27 $ (volume of the whole cube). The extra multiplication accounts for the third dimension!

Q: Can I use this formula for any cube?

Yes! The formula $ V = a^3 $ works for any cube, no matter how big or small. Just substitute the edge length and cube it.

Volume Calculation with Cubic Units

A cube has edges measuring 3 cm.

What is the volume of the cube?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:04 Calculate the volume of the cube.

00:07 We'll call the edge length A. In a cube, each edge is the same length.

00:13 Now, to find the volume, use the formula. Width times length times height.

00:23 Since all edges are equal, the formula becomes A times A times A.

00:31 Let's plug in the value for A and solve for the volume.

00:49 And that's how we find the volume of a cube!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

A cube has edges measuring 3 cm.

What is the volume of the cube?

Step-by-step solution

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

Identify the given information: The edge of the cube is 3 cm.
Apply the formula for the volume of a cube: $V = a^3$ .
Calculate the volume by substituting the given edge length into the formula.

Now, let's work through each step:

Step 1: The edge length $a$ is 3 cm.

Step 2: The formula for the volume of a cube is $V = a^3$ . Substituting the given edge length, we have:

$V = 3^3$

Step 3: Calculate $3^3$ :

$3 \times 3 \times 3 = 27$

Therefore, the volume of the cube is $27$ cubic centimeters.

Thus, the solution to the problem is $27$ cm $^3$ .

Final Answer

$27$

Key Points to Remember

Essential concepts to master this topic

Formula: Volume of cube equals edge length cubed: $V = a^3$
Calculation: For 3 cm edge: $3^3 = 3 \times 3 \times 3 = 27$
Units: Volume answer must include cubic units: 27 cm³ ✓

Common Mistakes

Avoid these frequent errors

Multiplying edge by 3 instead of cubing
Don't calculate 3 × 3 = 9 cm³! This gives area of one face, not volume. A cube has 3 dimensions, so you need all three: length × width × height. Always cube the edge length: 3³ = 27 cm³.

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 I cube the edge length instead of just squaring it?

Because volume measures 3-dimensional space! You need length × width × height. Since all edges are equal in a cube, that's edge × edge × edge = edge³.

What's the difference between cm² and cm³?

cm² measures area (flat surfaces like a square), while cm³ measures volume (space inside a 3D shape). Always use cubic units for volume!

How is 3³ different from 3 × 3?

$3^2 = 3 \times 3 = 9$ (area of one face), but $3^3 = 3 \times 3 \times 3 = 27$ (volume of the whole cube). The extra multiplication accounts for the third dimension!

Can I use this formula for any cube?

Yes! The formula $V = a^3$ works for any cube, no matter how big or small. Just substitute the edge length and cube it.

What if the edge length is a decimal or fraction?

The same formula works! For example, if the edge is 2.5 cm, then $V = (2.5)^3 = 2.5 \times 2.5 \times 2.5 = 15.625$ cm³.

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