Calculate the Volume of a Cube with 1cm Edge Length: Basic 3D Geometry

Q: Why is the volume 1 cm³ when the edge is also 1 cm?

Because volume measures 3-dimensional space! You multiply length × width × height: $ 1 \times 1 \times 1 = 1 $. The unit becomes cm³ because you're multiplying three lengths together.

Q: What does the ³ symbol mean in cm³?

The ³ (cubed) means three dimensions multiplied together. It shows this measurement is for volume (3D), not area (²) or length (no exponent).

Q: Is there a difference between 1 cubic cm and 1 cm³?

No difference at all! Both 1 cubic centimeter and 1 cm³ mean exactly the same thing - they're just different ways to write the same unit.

Q: How can I visualize what 1 cm³ looks like?

Picture a tiny cube where each edge is 1 centimeter long - about the width of your pinky fingernail! It's a very small amount of space.

Q: What if the edge length was 2 cm instead?

Then the volume would be $ 2^3 = 2 \times 2 \times 2 = 8 $ cm³. Notice how doubling the edge makes the volume 8 times bigger, not just 2 times!

Cube Volume with Unit Edge Length

The cube has edges measuring 1 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 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

00:21 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

The cube has edges measuring 1 cm long.

Calculate the volume of the cube.

Step-by-step solution

To solve this problem, we will follow a straightforward method.

Step 1: Identify the given information.
The problem states that the edge of the cube is 1 cm long.

Step 2: Apply the formula for the volume of a cube.
The volume $V$ of a cube with edge length $a$ is given by the formula: $V = a^3$

Step 3: Substitute the given edge length into the formula.
Substituting $a = 1$ cm into the formula gives: $V = 1^3$

Step 4: Perform the calculation.
Calculate $1^3$ , which equals 1.

Therefore, the volume of the cube is $1$ cm³.

Final Answer

$1$ cm³

Key Points to Remember

Essential concepts to master this topic

Formula: Volume of cube equals edge length cubed: $V = a^3$
Calculation: With edge = 1 cm, volume = $1^3 = 1$ cm³
Check: Any number to the third power: $1 \times 1 \times 1 = 1$ ✓

Common Mistakes

Avoid these frequent errors

Using wrong formula or confusing with surface area
Don't use $V = 6a^2$ (surface area formula) = 6 cm² instead of volume! Surface area measures the outside covering, not the space inside. Always use $V = a^3$ for cube volume.

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 is the volume 1 cm³ when the edge is also 1 cm?

Because volume measures 3-dimensional space! You multiply length × width × height: $1 \times 1 \times 1 = 1$ . The unit becomes cm³ because you're multiplying three lengths together.

What does the ³ symbol mean in cm³?

The ³ (cubed) means three dimensions multiplied together. It shows this measurement is for volume (3D), not area (²) or length (no exponent).

Is there a difference between 1 cubic cm and 1 cm³?

No difference at all! Both 1 cubic centimeter and 1 cm³ mean exactly the same thing - they're just different ways to write the same unit.

How can I visualize what 1 cm³ looks like?

Picture a tiny cube where each edge is 1 centimeter long - about the width of your pinky fingernail! It's a very small amount of space.

What if the edge length was 2 cm instead?

Then the volume would be $2^3 = 2 \times 2 \times 2 = 8$ cm³. Notice how doubling the edge makes the volume 8 times bigger, not just 2 times!

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