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

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

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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