Calculate Cube Volume: Finding Volume When Side Length is 2X

Q: Why do we cube the side length for volume?

Volume measures 3D space - length × width × height. Since a cube has all sides equal, we multiply the side length three times: side × side × side = side³.

Q: How do I handle the algebraic expression (2X)³?

Think of (2X) as one complete unit. When you cube it, apply the exponent to everything inside: $ (2X)^3 = 2^3 \times X^3 = 8X^3 $.

Q: What's the difference between 2X³ and (2X)³?

Order of operations matters! 2X³ means 2 × X³, but (2X)³ means (2X) × (2X) × (2X) = 8X³. The parentheses change everything!

Q: Can I check my answer without knowing what X equals?

Yes! Check that your expression makes sense: 8X³ has the right units (cubic units) and follows the pattern that doubling a side length should multiply volume by 8.

Q: Why is the answer 8X³ and not 6X³?

Because we cube everything: $ (2X)^3 = 2^3 \times X^3 $. Since 2³ = 8, we get 8X³. Don't confuse this with 2 × 3 = 6!

Volume Formulas with Algebraic Expressions

What is the volume of a cube with sides measuring 2X?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:04 Let's find the volume of the cube.

00:07 To do this, we use the formula: edge length to the power of three.

00:12 We'll plug in the edge length value and solve for the volume.

00:16 Then, calculate by raising the value to the power of three.

00:20 And that's how we find the cube's volume!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

What is the volume of a cube with sides measuring 2X?

Step-by-step solution

To find the volume of a cube, we use the formula:

$V = \text{side}^3$

Here, the side length of the cube is given as $2X$ . Substituting this into the formula gives:

$V = (2X)^3$

To expand this expression, apply the cube to every part of the expression:

$V = 2^3 \times X^3$

$V = 8 \times X^3$

Thus, the volume of the cube is:

$V = 8X^3$

Therefore, the correct answer is:

$8X^3$

Thus, the solution to the problem is $8x^3$ .

Final Answer

$8x^3$

Key Points to Remember

Essential concepts to master this topic

Cube Volume Formula: Volume equals side cubed: V = side³
Algebraic Cubing: (2X)³ = 2³ × X³ = 8X³
Verification: Check units match: length cubed gives cubic units ✓

Common Mistakes

Avoid these frequent errors

Cubing only the coefficient or only the variable
Don't cube just the 2 to get 8X or just the X to get 2X³! This ignores how exponents work with products. When cubing (2X), you must cube both parts: (2X)³ = 2³ × X³ = 8X³. Always apply the exponent to every factor inside the parentheses.

Practice Quiz

Test your knowledge with interactive questions

Find a,b

FAQ

Everything you need to know about this question

Why do we cube the side length for volume?

Volume measures 3D space - length × width × height. Since a cube has all sides equal, we multiply the side length three times: side × side × side = side³.

How do I handle the algebraic expression (2X)³?

Think of (2X) as one complete unit. When you cube it, apply the exponent to everything inside: $(2X)^3 = 2^3 \times X^3 = 8X^3$ .

What's the difference between 2X³ and (2X)³?

Order of operations matters! 2X³ means 2 × X³, but (2X)³ means (2X) × (2X) × (2X) = 8X³. The parentheses change everything!

Can I check my answer without knowing what X equals?

Yes! Check that your expression makes sense: 8X³ has the right units (cubic units) and follows the pattern that doubling a side length should multiply volume by 8.

Why is the answer 8X³ and not 6X³?

Because we cube everything: $(2X)^3 = 2^3 \times X^3$ . Since 2³ = 8, we get 8X³. Don't confuse this with 2 × 3 = 6!

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