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

00:00 Express the volume of the cube

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

00:07 We'll substitute appropriate values and solve for the volume

00:10 We'll raise each factor to the power and calculate

00:13 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

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

A cube has a total of 14 edges.

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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