Calculate Cube Edge Length: Finding Side Measurement from 1 cm³ Volume

Q: Why do we use cube root and not square root?

Because volume is three-dimensional! A cube has length × width × height, and since all sides are equal, we have a × a × a = a³. To undo cubing, we need the cube root.

Q: What if the volume isn't a perfect cube like 1?

You'll get a decimal answer! For example, if V = 2 cm³, then edge length = ∛2 ≈ 1.26 cm. Use a calculator for cube roots that aren't whole numbers.

Q: Can I check my answer without a calculator?

Yes! Simply multiply your answer by itself three times. If edge = 1 cm, then 1 × 1 × 1 = 1 cm³. This should equal the original volume.

Q: What does ∛ symbol mean?

The symbol ∛ means cube root - it asks 'what number times itself three times gives this result?' So ∛8 asks 'what number × itself × itself = 8?' The answer is 2.

Cube Volume with Edge Length Calculations

A cube has a volume of 1 cm3.

How long are the cube's edges?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find the cube's edge

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

00:07 We'll substitute appropriate values and solve for edge A

00:19 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 a volume of 1 cm3.

How long are the cube's edges?

Step-by-step solution

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

Step 1: Identify the formula for the volume of a cube.
Step 2: Apply the formula with given values.
Step 3: Calculate the cube root to find the edge length.

Now, let's work through each step:

Step 1: The volume of a cube is given by the formula $V = a^3$ , where $a$ is the edge length.

Step 2: We are given the volume $V = 1 \, \text{cm}^3$ . Therefore, we have $1 = a^3$ .

Step 3: To find $a$ , we take the cube root of both sides of the equation:

$a = \sqrt[3]{1} = 1 \, \text{cm}$ .

Thus, the edge length of the cube is $\mathbf{1 \, \text{cm}}$ .

Final Answer

$1$ cm

Key Points to Remember

Essential concepts to master this topic

Formula: Cube volume equals edge length cubed, V = a³
Technique: Take cube root of volume: ∛1 = 1 cm
Check: Verify by cubing the answer: 1³ = 1 cm³ ✓

Common Mistakes

Avoid these frequent errors

Using square root instead of cube root
Don't find √1 = 1 thinking it's the same as ∛1 = 1! While they equal 1 here, for other volumes like 8 cm³, √8 ≈ 2.8 but ∛8 = 2. Always use cube root for 3D volume problems.

Practice Quiz

Test your knowledge with interactive questions

Find a,b

FAQ

Everything you need to know about this question

Why do we use cube root and not square root?

Because volume is three-dimensional! A cube has length × width × height, and since all sides are equal, we have a × a × a = a³. To undo cubing, we need the cube root.

What if the volume isn't a perfect cube like 1?

You'll get a decimal answer! For example, if V = 2 cm³, then edge length = ∛2 ≈ 1.26 cm. Use a calculator for cube roots that aren't whole numbers.

How is this different from finding the side of a square?

Squares are 2D (area = side²), so you use square root. Cubes are 3D (volume = side³), so you use cube root. Different dimensions need different operations!

Can I check my answer without a calculator?

Yes! Simply multiply your answer by itself three times. If edge = 1 cm, then 1 × 1 × 1 = 1 cm³. This should equal the original volume.

What does ∛ symbol mean?

The symbol ∛ means cube root - it asks 'what number times itself three times gives this result?' So ∛8 asks 'what number × itself × itself = 8?' The answer is 2.

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