Volume of Rectangular Prisms Examples in Math

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

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 volume of a rectangular prism is the number of unit cubes that fill the solid, calculated by multiplying length, width, and height.

Imagine filling a box with small cubes — the total number of cubes is the volume.

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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: The volume of a rectangular prism is length times width times height — the count of unit cubes that fill it.

Common stuck point: The procedure for volume of rectangular prisms is the easy part; the trap is adding the dimensions instead of multiplying. Asking "Does the solid have three perpendicular dimensions, and is the answer in cubic units?" first is what keeps a correct-looking calculation from being attached to the wrong concept.

Sense of Study hint: Ask: Does the solid have three perpendicular dimensions, and is the answer in cubic units?

Worked Examples

Example 1

easy
Step-by-step: find the volume of a 6 × 5 × 2 box.

Answer

6060

First step

1
Identify l=6l=6, w=5w=5, h=2h=2.

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Example 2

medium
A fish tank is 50 cm × 40 cm × 30 cm. How many liters does it hold? (Use 1000 cm³ = 1 L.)

Example 3

medium
A rectangular prism has dimensions l=7l=7, w=3w=3, h=5h=5. Find both base area BB and volume VV.

Example 4

hard
A storage container is 2 m × 1.5 m × 1 m. Find its volume in m³, then in liters.

Example 5

hard
A toy chest is 0.8 m × 0.5 m × 0.4 m. Find its volume in cubic centimeters.

Example 6

challenge
A 5 × 4 × 3 box is fully packed with 1 × 1 × 1 unit cubes. If you remove the cubes that touch any outer face, how many cubes remain?

Practice Problems

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

Example 1

easy
Find the volume of a box 5 × 4 × 3.

Example 2

easy
Find the volume of a cube with edge 4.

Example 3

easy
A box has base area 15 and height 4. Find its volume.

Example 4

easy
How many unit cubes fit in a 2 × 2 × 2 box?

Example 5

easy
A box has volume 30 and base area 6. Find its height.

Example 6

easy
A cube has volume 27. Find its edge length.

Example 7

medium
A box is 10 cm × 4 cm × 3 cm. Find its volume in cm³.

Example 8

medium
A box is 8 × ww × 4 and has volume 96. Find ww.

Example 9

medium
A swimming pool is 25 m × 10 m × 2 m. Find its volume in m³.

Example 10

medium
How many 1 cm cubes fit in a 5 cm × 4 cm × 3 cm box?

Example 11

medium
A box has volume 240 cm³ and a square base of side 6 cm. Find the height.

Example 12

medium
A cube has volume 125 cm³. Find its edge length.

Example 13

medium
If each edge of a cube doubles, the volume multiplies by what factor?

Example 14

medium
How many 2 cm cubes fit in a 6 cm × 4 cm × 4 cm box?

Example 15

medium
A box is 12 × 5 × hh with volume 240 cm³. Find hh.

Example 16

hard
A box with square base of side ss and height 8 has volume 200. Find ss.

Example 17

hard
A 3 × 3 × 3 cube is painted on all faces, then cut into 1 × 1 × 1 unit cubes. How many unit cubes have NO paint?

Example 18

hard
Two boxes have the same volume. Box A is 6 × 4 × 5. Box B is a cube. Find the edge length of B (decimal OK).

Example 19

hard
A box of volume 150 has length 10 and width 5. Find the height.

Example 20

hard
A rectangular tank's length is doubled and its height is halved. The width is unchanged. How does the volume change?

Example 21

hard
A 4 × 4 × 4 cube is painted on all faces, then cut into unit cubes. How many unit cubes have paint on exactly two faces?

Example 22

challenge
A box has dimensions in ratio 1:2:31:2:3 and volume 162 cm³. Find the three dimensions.
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Background Knowledge

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

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