P6 Volume: The Complete Guide to Cubes and Cuboids

Volume is one of the most important topics in P6 Math. In this guide, we’ll master the formulas, learn how to work backwards, and tackle tricky word problems.

What is Volume?

Volume is the amount of space a 3D object occupies. For Primary 6 Math, we focus on two main solids: the Cube and the Cuboid.

The Formula

The formula for the volume of any rectangular box (cuboid) is simple:

$Volume = Length \times Breadth \times Height$

A cuboid with Length 6cm, Breadth 4cm, and Height 3cm.

For a Cube, since all sides are equal ( $Length = Breadth = Height$ ), the formula becomes:

$Volume = Edge \times Edge \times Edge$

A cube has all edges equal.

Finding Unknown Dimensions (Working Backwards)

One of the most common P6 exam questions gives you the Volume and two dimensions, and asks you to find the third.

We can rearrange the formula:

$Height = \frac{Volume}{Length \times Breadth}$ $Length = \frac{Volume}{Breadth \times Height}$ $Breadth = \frac{Volume}{Length \times Height}$

Example 1: Finding an Unknown Edge

Problem:

A rectangular tank has a volume of $3024 \text{ cm}^3$ . Its length is $18 \text{ cm}$ and its breadth is $14 \text{ cm}$ . Find its height.

Solution:

We know that $Volume = L \times B \times H$ .

To find Height: $H = \frac{Volume}{L \times B}$ $H = \frac{3024}{18 \times 14}$ $H = \frac{3024}{252}$ $H = 12 \text{ cm}$

Answer: The height is 12 cm.

For Cubes: Using Cube Roots

If you are given the volume of a cube and asked to find the edge, you need to find a number that, when multiplied by itself three times, equals the volume. This is called the cube root ( $\sqrt[3]{V}$ ).

💡 Common Perfect Cubes to Memorize

$1 \times 1 \times 1 = 1$
$2 \times 2 \times 2 = 8$
$3 \times 3 \times 3 = 27$
$4 \times 4 \times 4 = 64$
$5 \times 5 \times 5 = 125$
$6 \times 6 \times 6 = 216$
$7 \times 7 \times 7 = 343$
$8 \times 8 \times 8 = 512$
$9 \times 9 \times 9 = 729$
$10 \times 10 \times 10 = 1000$

The “Base Area” Connection

Sometimes questions won’t give you Length and Breadth separately. Instead, they might give you the Base Area.

Remember that $Base Area = Length \times Breadth$ .

So, the volume formula can be written as:

$Volume = Base Area \times Height$

And conversely:

$Height = \frac{Volume}{Base Area}$ $Base Area = \frac{Volume}{Height}$

Example 2: Using Base Area

Problem:

A container has a base area of $150 \text{ cm}^2$ and contains $2.4 \text{ litres}$ of water. Find the height of the water level.

Solution:

Step 1: Convert Litres to Cubic Centimeters ( $\text{cm}^3$ ) $1 \text{ litre} = 1000 \text{ cm}^3$ $2.4 \text{ litres} = 2400 \text{ cm}^3$

Step 2: Find Height $Height = \frac{Volume}{Base Area}$ $Height = \frac{2400}{150}$ $Height = 16 \text{ cm}$

Answer: The water level is 16 cm.

Common Mistakes in P6 Volume

⚠️ Mistake 1: Unit Conversion Errors

The most common mistake is forgetting to convert litres to $\text{cm}^3$ (or milliliters) before calculating dimensions.

Rule: Always work in $\text{cm}$ and $\text{cm}^3$ .

Volume in Litres $\times 1000 \rightarrow$ Volume in $\text{cm}^3$
Volume in $\text{m}^3 \times 1,000,000 \rightarrow$ Volume in $\text{cm}^3$ (Be careful with this one!)

⚠️ Mistake 2: Square Root vs Cube Root

For Area of a square face, you take the Square Root ( $\sqrt{Area}$ ).
For Volume of a cube, you take the Cube Root ( $\sqrt[3]{Volume}$ ).

Don’t mix them up! If Volume is $64 \text{ cm}^3$ , the edge is $4 \text{ cm}$ ( $4 \times 4 \times 4$ ), NOT $8 \text{ cm}$ ( $8 \times 8$ ).

Word Problem Strategy: Water Tanks

Water tank problems often involve water being poured in or out. The key is that the Base Area usually stays the same, only the Height of the water changes.

Strategy:

Draw a model or sketch if needed.
Calculate the Base Area first if possible.
Find the Volume of Water (convert from Litres if needed).
Use $Height = \frac{Volume}{Base Area}$ .

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P6 Volume: The Complete Guide to Cubes and Cuboids

P6 Volume: The Complete Guide to Cubes and Cuboids

What is Volume?

The Formula

Finding Unknown Dimensions (Working Backwards)

For Cubes: Using Cube Roots

The “Base Area” Connection

Common Mistakes in P6 Volume

Word Problem Strategy: Water Tanks

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