Volume Examples in Math

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Volume.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Math.

Concept Recap

The amount of three-dimensional space that an object occupies, measured in cubic units such as cm³.

How many cubic centimetre blocks would it take to completely fill the inside of the object?

Read the full concept explanation →

How to Use These Examples

  • Read the first worked example with the solution open so the structure is clear.
  • Try the practice problems before revealing each solution.
  • Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: Volume is three-dimensional—it is measured in cubic units such as cm³, m³, or in³.

Common stuck point: Units are cubed (\text{ft}^3, \text{m}^3, \text{cm}^3) because it's 3D.

Sense of Study hint: Try filling a box with unit cubes and counting them. Compare that count to the formula length times width times height.

Worked Examples

Example 1

easy
Find the volume of a rectangular prism with length 5 cm, width 3 cm, and height 4 cm.

Solution

  1. 1
    A rectangular prism (cuboid) has three mutually perpendicular dimensions. Its volume is the product of all three: V = l \times w \times h.
  2. 2
    Substitute the given dimensions — length l = 5 cm, width w = 3 cm, height h = 4 cm.
  3. 3
    Compute: V = 5 \times 3 \times 4 = 60 cm³. Units are cubic (cm³) because length × length × length = length³.

Answer

V = 60 \text{ cm}^3
Volume measures three-dimensional space. For a rectangular prism, it equals the product of its three dimensions. Volume is always in cubic units.

Example 2

medium
Find the volume of a cylinder with radius 3 cm and height 10 cm. Leave your answer in terms of \pi.

Example 3

medium
A cylindrical water tank has radius 3 m and height 5 m. Find its volume in cubic meters (leave answer in terms of \pi).

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

hard
A rectangular storage box is 8 cm long and 6 cm wide. If its volume is 336 cm³, find its height.

Example 2

medium
A cylinder has volume 200\pi cm³ and height 8 cm. Find its radius.
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Background Knowledge

These ideas may be useful before you work through the harder examples.

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