Solve for X: Finding Missing Dimension in Cuboid with Volume 45 and Height 4

Volume Formula with Unknown Dimensions

Given the cuboid of the figure:

444XXX2.52.52.5

Given: volume of the cuboid is 45

What is the value of X?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Determine the height of box X
00:03 Use the formula for calculating box volume
00:07 Width multiplied by Height multiplied by Length
00:13 Insert the appropriate values into the formula according to the given data and solve for X
00:18 Isolate X
00:23 Here is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Given the cuboid of the figure:

444XXX2.52.52.5

Given: volume of the cuboid is 45

What is the value of X?

2

Step-by-step solution

Volume formula for a rectangular prism:

Volume = length X width X height

Therefore, first we will place the data we are given into the formula:

45 = 2.5*4*X

We divide both sides of the equation by 2.5:

18=4*X

And now we divide both sides of the equation by 4:

4.5 = X

3

Final Answer

4.5

Key Points to Remember

Essential concepts to master this topic
  • Volume Formula: Volume = length × width × height for rectangular prisms
  • Technique: Substitute known values: 45 = 2.5 × 4 × X = 10X
  • Check: Verify by calculating: 2.5 × 4 × 4.5 = 45 ✓

Common Mistakes

Avoid these frequent errors
  • Forgetting to apply operations to both sides equally
    Don't divide only the left side by 10 when solving 45 = 10X = wrong equation! This violates the equality principle and gives incorrect results. Always perform the same operation to both sides of the equation.

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.

121212888555

FAQ

Everything you need to know about this question

Which dimension represents length, width, and height in the diagram?

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From the diagram: length = 2.5 (labeled on the right edge), width = 4 (labeled at the bottom), and height = X (labeled on the left side). The order doesn't matter for multiplication!

Why do I multiply all three dimensions together?

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Volume measures how much space is inside a 3D shape. You need all three dimensions because you're finding how many unit cubes fit inside the rectangular prism.

What if I get a decimal answer like 4.5?

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Decimal answers are completely normal for geometry problems! Real-world measurements often involve fractions and decimals. Just make sure your calculation is correct.

How can I double-check my work?

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Substitute your answer back: 2.5 × 4 × 4.5. First calculate 2.5 × 4 = 10, then 10 × 4.5 = 45. If you get the original volume, you're right!

What if I mixed up which number goes where?

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Good news! Since volume uses multiplication, the order doesn't matter. Whether you write 2.5 × 4 × X or 4 × X × 2.5, you'll get the same answer.

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