---
title: "Volume of cuboids"
description: "Find the volume of right rectangular prisms by packing with unit cubes and show it equals l × w × h (or base area × height); apply V = l × w × h and V = B × h to solve real-world problems; calculate, "
canonical: https://lightmysky.com/learn/mathematics/volume-of-cuboids-mt_nTL-owFJTF
source: https://lightmysky.com/learn/mathematics/volume-of-cuboids-mt_nTL-owFJTF.md
retrieved: 2026-10-19
---

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# Volume of cuboids

Find the volume of right rectangular prisms by packing with unit cubes and show it equals l × w × h (or base area × height); apply V = l × w × h and V = B × h to solve real-world problems; calculate, estimate, and compare volumes of cubes and cuboids in standard units (cm³, m³)

Subject: Mathematics · Area: Measurement · Ages 10 to 11
Page: https://lightmysky.com/learn/mathematics/volume-of-cuboids-mt_nTL-owFJTF

## Ready when they can

- Use V = l × w × h to find the volume of a cuboid 4 cm × 3 cm × 5 cm = 60 cm³
- Explain why packing a prism with unit cubes gives the same result as multiplying edge lengths
- Compare volumes of two cuboids and identify which has greater capacity

## Lesson: Finding the volume of a box

You already know how to fill a box with unit cubes and count them. There is a faster way. For a box shaped like a rectangle (a cuboid), multiply the length, the width, and the height to tell fast which box holds more: V = l × w × h.

*(drawing: This bottom layer has 3 rows of 4 cubes, so 12 cubes cover the base. Stack 5 layers like this and you get 60 cubes in all.)*

**Example.** A box is 4 cm long, 3 cm wide, and 5 cm tall. Multiply the three numbers: 4 × 3 × 5 = 60. The volume is 60 cm³.

Packing cubes one by one gives the same answer as multiplying, because each layer holds l × w cubes and there are h layers stacked up. If you already know the area of the base, call it B, you can use V = B × h instead. For small things use cm³. For very large things, like a swimming pool, use m³.

**Example.** Box A is 30 cm long, 20 cm wide, 25 cm tall: 30 × 20 × 25 = 15,000 cm³. Box B is 25 cm long, 25 cm wide, 20 cm tall: 25 × 25 × 20 = 12,500 cm³. Box A holds more.

**Recap.** Multiply length × width × height, or base area × height, to find a box's volume in cubic units like cm³ or m³.

## Practice

16 questions on this page, each with its working shown.

## Needs first

- [Counting Unit Cubes](https://lightmysky.com/learn/mathematics/counting-unit-cubes-mt_d7XktBQPxm)
- [Long multiplication (age 10+)](https://lightmysky.com/learn/mathematics/long-multiplication-age-10-mt_XLP1IM3Qbb)

## Opens up

- [Volume as additive](https://lightmysky.com/learn/mathematics/volume-as-additive-mt_5TBUFnCy5-)
- [Using a Calculator Well](https://lightmysky.com/learn/mathematics/using-a-calculator-well-mt_FZE80D2jS_)
- [Volume and Surface Area of Prisms and Cylinders](https://lightmysky.com/learn/mathematics/volume-and-surface-area-of-prisms-and-cylinders-mt_JTLJ5LDrYh)
- [Area and volume formulae](https://lightmysky.com/learn/mathematics/area-and-volume-formulae-mt_tAJH5BrpOx)
- [Real-World Mathematical Modelling](https://lightmysky.com/learn/mathematics/real-world-mathematical-modelling-mt_yqZiX6vS7D)