Calculate the Volume of a Cube with 2 cm Edges: Step-by-Step Solution

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

A cube has three dimensions: length × width × height. Since all edges are equal (2 cm each), we calculate $ 2 \times 2 \times 2 = 2^3 = 8 $. Multiplying by 3 would give us the perimeter of one face, not the volume!

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

cm² measures area (flat surfaces like squares), while cm³ measures volume (3D space inside objects). Since we're finding how much space is inside the cube, we need cm³.

Q: How can I remember the cube volume formula?

Think of it as "edge × edge × edge" since you're filling a 3D box. You can also remember: cube volume uses cubed numbers ($ s^3 $)!

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

The same formula works! Calculate $ 2.5^3 = 2.5 \times 2.5 \times 2.5 = 15.625 $ cm³. Just be careful with your decimal multiplication.

Volume Calculations with Perfect Cube Numbers

A cube has edges measuring 2 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 will use the formula for calculating cube volume (edge length cubed):

00:07 Edge length according to the given data

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

00:16 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 2 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 - The edge length of the cube is 2 cm.
Step 2: Apply the appropriate formula to find the volume of the cube.
Step 3: Perform the calculation with the given edge length.

Now, let's work through each step:
Step 1: The problem provides that each edge of the cube measures 2 cm.
Step 2: The formula for the volume of a cube is $V = s^3$ , where $s$ is the edge length.
Step 3: Plugging in the values, we calculate the volume as follows:

V = 2^3 = 2 \times 2 \times 2 = 8 \text{ cm}^3

Therefore, the volume of the cube is $\mathbf{8 \, \text{cm}^3}$ .

Final Answer

$8$ cm³

Key Points to Remember

Essential concepts to master this topic

Formula: Volume of a cube equals edge length cubed: $V = s^3$
Calculation: With edge = 2 cm: $V = 2^3 = 2 \times 2 \times 2 = 8$
Check: Units must be cubic: 8 cm³ makes sense for 3D volume ✓

Common Mistakes

Avoid these frequent errors

Using wrong formula or forgetting to cube the edge length
Don't calculate $V = s^2$ (area formula) or $V = 3s$ = wrong answer! These give 4 cm² or 6 cm instead of 8 cm³. Always use $V = s^3$ for cube volume and multiply the edge by itself three times.

Practice Quiz

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FAQ

Everything you need to know about this question

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

A cube has three dimensions: length × width × height. Since all edges are equal (2 cm each), we calculate $2 \times 2 \times 2 = 2^3 = 8$ . Multiplying by 3 would give us the perimeter of one face, not the volume!

What's the difference between cm² and cm³?

cm² measures area (flat surfaces like squares), while cm³ measures volume (3D space inside objects). Since we're finding how much space is inside the cube, we need cm³.

How can I remember the cube volume formula?

Think of it as "edge × edge × edge" since you're filling a 3D box. You can also remember: cube volume uses cubed numbers ( $s^3$ )!

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

The same formula works! Calculate $2.5^3 = 2.5 \times 2.5 \times 2.5 = 15.625$ cm³. Just be careful with your decimal multiplication.

Can I check my answer another way?

Yes! Think about it logically: if one small 1 cm³ cube fits in each corner, how many fit total? A 2×2×2 arrangement gives you 8 small cubes, confirming our answer of 8 cm³.

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