PSLE Volume: Complete Guide to Cube and Cuboid Problems

Volume questions appear in almost every PSLE Math paper. Master the formulas, learn to find unknown dimensions, and conquer water tank problems with this comprehensive guide.

Why Volume Is Essential for PSLE

Volume tells us how much space a 3D shape takes up. In PSLE, volume questions typically appear in Paper 2 and can be worth 3-5 marks each. The good news? Once you understand the core formulas and relationships, these problems become very manageable.

In this guide, we’ll cover:

Volume formulas for cubes and cuboids
Finding unknown dimensions when given volume
Using face area to solve problems
Water tank problems with litres and cm³ conversion
Multi-step problems combining multiple concepts

The Essential Formulas

Cuboid

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

or V = L x B x H

A cuboid has 3 different dimensions

Cube

$\text{Volume} = \text{Side} \times \text{Side} \times \text{Side} = \text{Side}^3$

All edges are equal!

A cube has all edges equal

Alternative Formula Using Base Area:

$\text{Volume} = \text{Base Area} \times \text{Height}$

This is helpful when you’re given the base area directly!

Type 1: Calculating Volume

The most straightforward type—you’re given dimensions and need to find the volume.

Example 1: Volume of a Cuboid

Problem:

Find the volume of a cuboid with length 8 cm, breadth 5 cm, and height 6 cm.

Cuboid with dimensions 8 cm × 5 cm × 6 cm

Volume = Length x Breadth x Height
Volume = 8 x 5 x 6
Volume = 40 x 6 = 240 cm³

Example 2: Volume of a Cube

Problem:

A cube has edges of length 9 cm. What is its volume?

Cube with edge 9 cm

Volume = Side x Side x Side = Side³
Volume = 9 x 9 x 9
Volume = 81 x 9 = 729 cm³

💡 Perfect Cubes to Remember

2³ = 83³ = 274³ = 645³ = 1256³ = 2167³ = 3438³ = 5129³ = 72910³ = 100011³ = 133112³ = 172813³ = 2197

Type 2: Finding Unknown Dimensions

When you know the volume and some dimensions, you can work backwards to find the missing dimension using division.

Key Formulas:

Height = Volume / (Length x Breadth)
Length = Volume / (Breadth x Height)
Breadth = Volume / (Length x Height)
For cube: Side = cube root of Volume

Example 3: Finding the Height

Problem:

A cuboid has a volume of 360 cm³. Its length is 9 cm and its breadth is 8 cm. Find its height.

Find the missing height

Height = Volume / (Length x Breadth)
Height = 360 / (9 x 8)
Height = 360 / 72 = 5 cm

Example 4: Finding the Edge of a Cube

Problem:

A cube has a volume of 512 cm³. What is the length of one edge?

For a cube: Volume = Side³
Side = cube root of Volume = cube root of 512
Think: What number x itself x itself = 512?
8 x 8 x 8 = 512
Edge = 8 cm

💡 Tip for Finding Cube Roots

In PSLE, cube roots are always perfect cubes. Memorize the perfect cubes from 1³ to 13³ to quickly identify them!

Type 3: Using Base Area

Sometimes you’re given the base area instead of length and breadth separately. Remember: Volume = Base Area x Height

Example 5: Finding Height from Base Area

Problem:

The base area of a cuboid is 84 cm² and its volume is 1260 cm³. Find the height.

Base Area = 84 cm², Volume = 1260 cm³

Volume = Base Area x Height
Height = Volume / Base Area
Height = 1260 / 84 = 15 cm

Example 6: Finding Face Area of a Cube

Problem:

A cube has a volume of 1728 cm³. Find the area of one face.

Step 1: Find the edge length
Edge = cube root of 1728 = 12 cm (since 12 x 12 x 12 = 1728)
Step 2: Find face area
Face Area = Edge x Edge = 12 x 12 = 144 cm²

💡 Two-Step Process for Cube Face Area

Find edge using cube root: Edge = cube root of Volume
Square the edge: Face Area = Edge²

Type 4: Water Tank Problems

Water tank problems are PSLE favorites! They combine volume concepts with unit conversion.

Critical Conversion

$1 \text{ litre} = 1000 \text{ cm}^3$

To convert: litres x 1000 = cm³ | cm³ / 1000 = litres

Example 7: Finding Water Level Height

Problem:

A rectangular tank measures 50 cm by 30 cm by 40 cm. It contains 36 litres of water. What is the height of the water level?

Tank dimensions: 50 cm × 30 cm × 40 cm

Step 1: Convert litres to cm³
36 litres = 36 x 1000 = 36,000 cm³
Step 2: Find base area
Base Area = 50 x 30 = 1500 cm²
Step 3: Find water height
Water Height = Volume / Base Area = 36,000 / 1500 = 24 cm

Example 8: Water Needed to Fill Tank

Problem:

A rectangular tank measures 55 cm by 40 cm by 30 cm. It contains 44 litres of water. How many more litres are needed to fill it to the brim?

Step 1: Find total tank volume
Tank Volume = 55 x 40 x 30 = 66,000 cm³ = 66 litres
Step 2: Find water needed
Water needed = 66 - 44 = 22 litres

Type 5: Fractional Fill Problems

When a tank is fractionally filled, multiply the fraction by the total height (or volume) to find the water level.

Example 9: Fractional Fill

Problem:

A rectangular tank measures 48 cm by 36 cm by 50 cm. It is $\frac{3}{5}$ filled with water. How many litres of water does it contain?

Step 1: Find water height
Water height = $\frac{3}{5}$ x 50 = 30 cm
Step 2: Find water volume
Water Volume = 48 x 36 x 30 = 51,840 cm³
Step 3: Convert to litres
51,840 / 1000 = 51.84 litres

Type 6: Water Transfer Problems

When water is poured from one container to another, the volume stays constant. Use this to find the new water level.

Example 10: Water Transfer Between Tanks

Problem:

Tank P measures 50 cm by 40 cm by 36 cm and is completely filled with water. All the water is poured into empty Tank Q measuring 60 cm by 48 cm by 30 cm. What is the height of the water level in Tank Q?

Step 1: Find volume of water from Tank P
Water Volume = 50 x 40 x 36 = 72,000 cm³
Step 2: Find base area of Tank Q
Base Area = 60 x 48 = 2,880 cm²
Step 3: Find water height in Tank Q
Water Height = 72,000 / 2,880 = 25 cm

💡 Key Insight

The water height (25 cm) is less than Tank Q’s height (30 cm), so the water fits. Always check this!

Common Mistakes to Avoid

❌ Mistake 1: Forgetting Unit Conversion

Always convert litres to cm³ before calculating! 1 litre = 1000 cm³ (not 100!)

❌ Mistake 2: Confusing cm² and cm³

Area uses cm² (square), Volume uses cm³ (cubic)

❌ Mistake 3: Using Tank Height Instead of Water Height

The water level may be different from the tank’s total height!

❌ Mistake 4: Wrong Order of Operations

For Height = Volume / (L x B), calculate L x B first, then divide!

Quick Reference Table

Find	Formula
Volume (cuboid)	L x B x H
Volume (cube)	Side³
Height	Volume / (L x B) or Volume / Base Area
Base Area	Volume / Height
Edge (cube)	cube root of Volume
Face Area (cube)	Edge² (after finding edge from cube root of Volume)
Litres to cm³	Litres x 1000

PSLE-Style Challenge Problem

Challenge:

A rectangular tank measures 75 cm by 48 cm by 40 cm and is $\frac{5}{8}$ filled with water.

(a) How many litres of water are in the tank?

(b) If water is added at a rate of 6 litres per minute, how long will it take to fill the tank completely?

Click to reveal solution

Part (a):

Total tank volume = 75 x 48 x 40 = 144,000 cm³ = 144 litres

Water in tank = $\frac{5}{8}$ x 144 = 90 litres

Part (b):

Water needed = 144 - 90 = 54 litres

Time = Volume / Rate = 54 / 6 = 9 minutes

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PSLE Volume: Complete Guide to Cube and Cuboid Problems

PSLE Volume: Complete Guide to Cube and Cuboid Problems

Why Volume Is Essential for PSLE

The Essential Formulas

Type 1: Calculating Volume

Type 2: Finding Unknown Dimensions

Type 3: Using Base Area

Type 4: Water Tank Problems

Type 5: Fractional Fill Problems

Type 6: Water Transfer Problems

Common Mistakes to Avoid

Quick Reference Table

PSLE-Style Challenge Problem

Ready to Practice Volume Problems?

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