Calculate the Volume of a 7cm × 3cm × 5cm Cuboid: Step-by-Step Solution

Cuboid Volume with Three-Dimensional Multiplication

Calculate the volume of the cuboid

If its length is equal to 7 cm:

Its width is equal to 3 cm:

Its height is equal to 5 cm:

333777555

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Calculate the box volume
00:03 We'll use the formula for calculating box volume
00:07 width times height times length
00:13 We'll substitute appropriate values and solve for the volume
00:17 And this is the solution to the problem

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Calculate the volume of the cuboid

If its length is equal to 7 cm:

Its width is equal to 3 cm:

Its height is equal to 5 cm:

333777555

2

Step-by-step solution

The formula to calculate the volume of a cuboid is:

height*length*width

We replace the data in the formula:

3*5*7

7*5 = 35

35*3 = 105

3

Final Answer

105 cm³

Key Points to Remember

Essential concepts to master this topic
  • Formula: Volume equals length × width × height (all dimensions)
  • Technique: Multiply step-by-step: 7 × 3 = 21, then 21 × 5 = 105
  • Check: Units must be cubic (cm³) and all dimensions used once ✓

Common Mistakes

Avoid these frequent errors
  • Adding dimensions instead of multiplying
    Don't add 7 + 3 + 5 = 15 cm³! Addition gives perimeter or surface measurements, not volume. Volume requires space filling, so you need to multiply all three dimensions. Always multiply length × width × height for cuboid volume.

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 numbers instead of adding them?

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Volume measures space inside the cuboid! Think of it like stacking unit cubes: you need 7 rows of 3 columns of 5 layers. Adding would just give you the total distance around edges.

Does the order of multiplication matter?

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No! You can multiply length × width × height in any order you want. Whether you do 7 × 3 × 5 or 5 × 7 × 3, you'll always get 105 cm³.

Why is the answer in cubic centimeters (cm³)?

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Because we're measuring three-dimensional space! When you multiply cm × cm × cm, you get cm³. Volume always uses cubic units like cm³, m³, or ft³.

What if I forget one of the dimensions?

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You'll get the wrong answer! For example, 7 × 3 = 21 cm² is just the area of one face. You must use all three dimensions: length, width, AND height.

How can I remember the volume formula?

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Think "L × W × H" or imagine filling the box with tiny cubes. You need to count cubes in all three directions: how many across, how many deep, how many tall.

What's the difference between area and volume?

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Area uses 2 dimensions (like length × width = cm²) for flat surfaces. Volume uses 3 dimensions (length × width × height = cm³) for solid objects that take up space.

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