Calculate Cuboid Volume: Finding Space in an 8×5×12 Rectangular Prism

Cuboid Volume with Rectangular Dimensions

Look at the cuboid below:

888555121212

What is the volume of the cuboid?

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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 multiplied by Height multiplied by Length
00:12 Substitute appropriate values into the formula according to the given data and solve for the volume
00:46 Here is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Look at the cuboid below:

888555121212

What is the volume of the cuboid?

2

Step-by-step solution

To determine the volume of a cuboid, we apply the formula:

  • Step 1: Identify the dimensions of the cuboid:
    • Length (l l ) = 12 cm
    • Width (w w ) = 8 cm
    • Height (h h ) = 5 cm
  • Step 2: Apply the volume formula for a cuboid:

The formula to find the volume (V V ) of a cuboid is:

V=l×w×h V = l \times w \times h

Step 3: Substitute the given dimensions into the formula and calculate: V=12×8×5 V = 12 \times 8 \times 5

Step 4: Perform the multiplication in stages for clarity:

First, calculate 12×8=96 12 \times 8 = 96

Then multiply the result by 5: 96×5=480 96 \times 5 = 480

Therefore, the volume of the cuboid is 480cm3\mathbf{480 \, \text{cm}^3}.

3

Final Answer

480 cm³

Key Points to Remember

Essential concepts to master this topic
  • Formula: Volume = length × width × height for all cuboids
  • Technique: Calculate step-by-step: 12 × 8 = 96, then 96 × 5 = 480
  • Check: Units must be cubic (cm³) and answer should be reasonable ✓

Common Mistakes

Avoid these frequent errors
  • Adding dimensions instead of multiplying
    Don't add 12 + 8 + 5 = 25 cm³! This gives you perimeter thinking, not volume. Volume measures 3D space inside the cuboid. Always multiply all three dimensions: length × width × height.

Practice Quiz

Test your knowledge with interactive questions

Look at the cuboid below:

888555121212

What is the volume of the cuboid?

FAQ

Everything you need to know about this question

Why do we multiply all three dimensions instead of adding them?

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Volume measures the space inside a 3D shape. Think of it like stacking unit cubes - you need length × width × height layers. Adding would give you the total of the edges, not the space!

Does it matter which dimension I call length, width, or height?

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No! Multiplication is commutative, so 12 × 8 × 5 = 8 × 12 × 5 = 5 × 8 × 12. The volume will always be the same regardless of order.

What if I forget to include the cubic units (cm³)?

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Always include cubic units for volume! Since you're multiplying three lengths (cm × cm × cm), the result must be cm³. Without units, your answer is incomplete.

How can I remember the volume formula?

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Think of filling a box with unit cubes. You need to know how many cubes fit along each direction, then multiply to find the total: V=l×w×h V = l \times w \times h

What's the difference between a cuboid and a cube?

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A cube has all sides equal, while a cuboid can have different dimensions. Both use the same volume formula, but a cube would be V=s3 V = s^3 where s is the side length.

Is 480 cm³ a reasonable answer for this cuboid?

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Yes! The cuboid is fairly large (12×8×5 cm), so 480 cm³ makes sense. That's about half a liter of space, which matches the size shown in the diagram.

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