Calculate the Volume of a Cuboid with Dimensions 5×9×4 Units

Volume Calculations with Three-Dimensional Measurements

Given the cuboid of the figure:

555999444

What is its volume?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Calculate the volume of the box
00:03 We'll use the formula for calculating box volume
00:07 Width times height times length
00:11 We'll substitute appropriate values according to the given data and solve for the volume
00:26 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Given the cuboid of the figure:

555999444

What is its volume?

2

Step-by-step solution

To solve this problem, we'll calculate the volume of the cuboid using the given dimensions:

  • Step 1: Identify the dimensions
  • Step 2: Apply the volume formula for a cuboid
  • Step 3: Calculate the volume

Let's work through these steps:

Step 1: From the diagram, we are informed of two dimensions directly: the width w=5 w = 5 and the height h=4 h = 4 . The diagram also indicates the horizontal length (along the base) is l=9 l = 9 .

Step 2: To find the volume of the cuboid, we use the formula:
Volume=length×width×height.\text{Volume} = \text{length} \times \text{width} \times \text{height}.

Step 3: Substituting the identified dimensions into the formula, we have:
Volume=9×5×4.\text{Volume} = 9 \times 5 \times 4.

Calculating this, we find:
9×5=45,9 \times 5 = 45,
45×4=180.45 \times 4 = 180.

Therefore, the volume of the cuboid is 180180 cubic units.

This corresponds to choice \#4: 180.

3

Final Answer

180

Key Points to Remember

Essential concepts to master this topic
  • Formula: Volume of cuboid equals length × width × height
  • Technique: Multiply dimensions step by step: 9 × 5 = 45, then 45 × 4 = 180
  • Check: Units should be cubic (volume), and result makes sense for given dimensions ✓

Common Mistakes

Avoid these frequent errors
  • Adding dimensions instead of multiplying
    Don't add 9 + 5 + 4 = 18! This gives perimeter thinking, not volume. Volume measures space inside, which requires all three dimensions working together. Always multiply length × width × height for cuboid volume.

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

Does the order of multiplication matter for volume?

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No! You can multiply the dimensions in any order. Whether you do 9 × 5 × 4 or 4 × 9 × 5, you'll get the same answer: 180 cubic units.

What if the dimensions have different units?

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All dimensions must be in the same units before multiplying. If one is in meters and another in centimeters, convert them first. The final answer will be in cubic units.

How is this different from finding area?

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Area uses two dimensions (length × width) and gives square units. Volume uses three dimensions (length × width × height) and gives cubic units. Volume measures how much space is inside!

What does 180 cubic units actually mean?

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It means you could fit 180 unit cubes (each 1×1×1) inside this cuboid. Think of it like 180 small building blocks filling up the entire space!

Can I use this formula for any box shape?

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Yes! This formula works for any rectangular prism or cuboid. The faces must be rectangles with right angles at all corners.

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