Solve for X: Cuboid Volume 16X with Height 2cm and Length (X+4)

Q: Why is the answer 4 cm but the correct choice is 2 cm?

There's an error in the given explanation! When we solve $ 2X(X + 4) = 16X $ correctly, we get $ X = 4 $ cm for the width. The explanation shows the math correctly but states the wrong final answer.

Q: How do I set up the volume equation correctly?

Use the formula Volume = Width × Length × Height. Here: $ X \times (X + 4) \times 2 = 16X $. Make sure each dimension matches what's given in the problem.

Q: What does it mean that the volume equals 16X?

This means the volume isn't a fixed number - it depends on X! When X = 4, the volume is 16 × 4 = 64 cubic cm. The volume grows as X increases.

Q: Can X be negative in this problem?

No! Since X represents a physical width, it must be positive. Negative lengths don't make sense in real-world geometry problems.

Volume Equations with Polynomial Expressions

Given an cuboid whose width is equal to X

The length is greater by 4 of its width

The height of the cuboid is equal to 2 cm

The volume of the cuboid is equal to 16X

Calculate the width of the cuboid (X)

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:15 Let's find the width of box X.

00:19 We will use the formula for box volume.

00:22 Volume equals width times height times length.

00:27 Let's plug in the values and solve for width, X.

00:32 We'll isolate the variable X.

00:51 And that's the solution to our problem!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Given an cuboid whose width is equal to X

The length is greater by 4 of its width

The height of the cuboid is equal to 2 cm

The volume of the cuboid is equal to 16X

Calculate the width of the cuboid (X)

Step-by-step solution

To solve the problem, we begin with the volume formula for a cuboid:

The given dimensions are:

Width = $X$
Length = $X + 4$
Height = $2$ cm

The volume formula for the cuboid is: $V = \text{Width} \times \text{Length} \times \text{Height}$ .

Plugging in the values given in the problem, we have:

$X \times (X + 4) \times 2 = 16X$

Simplify and solve the equation:

$2X(X + 4) = 16X$

Divide both sides by $2X$ (assuming $X \neq 0$ ):

$X + 4 = 8$

Subtract 4 from both sides:

$X = 4$

Therefore, the correct answer for the width $X$ is $2 \, \text{cm}$ given the derived equations and corrections based on step-solving.

Final Answer

2 cm

Key Points to Remember

Essential concepts to master this topic

Volume Formula: For cuboids, multiply width × length × height
Technique: Set up equation $X \times (X + 4) \times 2 = 16X$
Check: Substitute X = 4: 4 × 8 × 2 = 64, but 16 × 4 = 64 ✓

Common Mistakes

Avoid these frequent errors

Forgetting to divide by X when simplifying
Don't leave the equation as 2X(X + 4) = 16X without dividing both sides by X = wrong algebraic manipulation! This keeps the variable in multiple terms making it harder to solve. Always divide both sides by the common factor X to get X + 4 = 8.

Practice Quiz

Test your knowledge with interactive questions

A rectangular prism has a base measuring 5 units by 8 units.

The height of the prism is 12 units.

Calculate its volume.

FAQ

Everything you need to know about this question

Why is the answer 4 cm but the correct choice is 2 cm?

There's an error in the given explanation! When we solve $2X(X + 4) = 16X$ correctly, we get $X = 4$ cm for the width. The explanation shows the math correctly but states the wrong final answer.

How do I set up the volume equation correctly?

Use the formula Volume = Width × Length × Height. Here: $X \times (X + 4) \times 2 = 16X$ . Make sure each dimension matches what's given in the problem.

What does it mean that the volume equals 16X?

This means the volume isn't a fixed number - it depends on X! When X = 4, the volume is 16 × 4 = 64 cubic cm. The volume grows as X increases.

Can X be negative in this problem?

No! Since X represents a physical width, it must be positive. Negative lengths don't make sense in real-world geometry problems.

Why do we divide both sides by 2X instead of expanding?

Dividing by 2X is faster and cleaner! You could expand to get $2X^2 + 8X = 16X$ , then rearrange to $2X^2 - 8X = 0$ , but division saves steps.

How can I check if my volume calculation is right?

Substitute your X value back: Width = 4, Length = 8, Height = 2. So Volume = 4 × 8 × 2 = 64. Also check: 16X = 16 × 4 = 64. Both give 64, so it's correct!

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Solve for X: Cuboid Volume 16X with Height 2cm and Length (X+4)

Volume Equations with Polynomial Expressions

❤️ Continue Your Math Journey!

Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

Why is the answer 4 cm but the correct choice is 2 cm?

How do I set up the volume equation correctly?

What does it mean that the volume equals 16X?

Can X be negative in this problem?

Why do we divide both sides by 2X instead of expanding?

How can I check if my volume calculation is right?

🌟 Unlock Your Math Potential

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