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

Calculate the volume of the rectangular prism below using the data provided.

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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