Volumes of cuboids Revision Notes for Edexcel GCSE Maths

Volumes of cuboids

What is volume?

Volume is the amount of space that a 3-D shape takes up. When we calculate volume, we're measuring how much space is inside a three-dimensional object.

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The most commonly used units for measuring volume are:

cm³ (cubic centimetres)
m³ (cubic metres)
Litres (where 1 litre = 1000 cm³)

Volume formula for cuboids

A cuboid is a 3-D shape with rectangular faces. To find the volume of any cuboid, you need to know its three dimensions: length, width, and height.

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Volume Formula for Cuboids:

$\text{Volume} = \text{Length} \times \text{Width} \times \text{Height}$

This formula works because you're essentially counting how many unit cubes fit inside the shape. Each dimension tells you how many cubes stretch in that direction.

Converting between units

When working with volume calculations, you may need to convert between different units:

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Key Unit Conversions:

1 litre = 1000 cm³
To convert from cm³ to litres: divide by 1000
To convert from litres to cm³: multiply by 1000

Worked examples

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Worked Example 1: Basic volume calculation

A wooden planting box has dimensions 160 cm × 70 cm × 15 cm.

Step 1: Apply the volume formula $\text{Volume} = 160 \times 70 \times 15 = 168,000 \text{ cm}^3$

Step 2: Convert to litres (if needed) $168,000 \div 1000 = :success[168 \text{ litres}]$

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Worked Example 2: Working with metres

A cuboid has dimensions 3.2 m × 1.5 m × 2.0 m.

$\text{Volume} = 3.2 \times 1.5 \times 2.0 = :success[9.6 \text{ m}^3]$

Notice that when the measurements are in metres, the volume is in cubic metres (m³).

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Worked Example 3: Finding a missing dimension

A cuboid has a volume of 390 cm³, with length 15 cm and width 4 cm. Find the height.

Using the formula: $\text{Volume} = \text{Length} \times \text{Width} \times \text{Height}$

$390 = 15 \times 4 \times h$ $390 = 60 \times h$ $h = 390 \div 60 = :success[6.5 \text{ cm}]$

Solving multi-step problems

Some exam questions combine volume calculations with other mathematical concepts like cost or quantity. Here's a systematic approach:

Calculate the volume using the formula
Convert units if necessary (e.g., cm³ to litres)
Apply the context (e.g., work out quantities or costs)
Round appropriately for real-world contexts

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Worked Example: Cost calculation

If a 50-litre bag of compost costs £3.99, and you need to fill the planting box from Example 1 (168 litres):

Step 1: Calculate bags needed $\text{Number of bags needed} = 168 \div 50 = 3.36 \text{ bags}$

Step 2: Round up to whole bags Since you can only buy whole bags, you need 4 bags

Step 3: Calculate total cost $\text{Total cost} = 4 \times £3.99 = :success[£15.96]$

Exam tips

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Critical Exam Success Tips:

Always check your units - make sure length, width, and height are in the same units before calculating
Show your working clearly, especially the formula you're using
When dealing with real-world problems, remember you often need to round up to whole numbers
Double-check your arithmetic, especially when multiplying three numbers together
Look out for unit conversions - the question might give dimensions in different units

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Key Points to Remember:

Volume measures the space inside a 3-D shape
Volume of a cuboid = Length × Width × Height
Common units are cm³, m³, and litres (1 litre = 1000 cm³)
Always use the same units for all dimensions before calculating
Multi-step problems require careful planning and clear working

Volumes of cuboids (Edexcel GCSE Maths): Revision Notes