Word Problems: Volume of Cube and Cuboid

Apply your volume skills to real-world problems involving containers and tanks

Important Unit Conversion

1 litre = 1000 cm³

Also: 1 ml = 1 cm³

This conversion is essential for water tank problems!

1. Basic Volume Word Problems

Problem-Solving Strategy

Identify what you're asked to find
Draw or visualise the shape
Write down the formula you need
Substitute the known values
Calculate and include units in your answer

Example 1: Finding Dimensions

Xinyi has a rectangular first-aid box with a volume of 1080 cm³. The length of the box is 15 cm and its height is 6 cm. What is the breadth of the box?

First-aid box: Volume = 1080 cm³

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Solution:

Volume = 1080 cm³, Length = 15 cm, Height = 6 cm

Breadth of cuboid = Volume ÷ (Length × Height)

$= \frac{1080}{15 \times 6}$

$= \frac{1080}{90}$

= 12 cm

The breadth of the first-aid box is 12 cm.

2. Water Tank Problems

Water Level in Tanks

When water is poured into a rectangular tank:

Volume of water = Length × Breadth × Water Height

Water Height = Volume of water ÷ (Length × Breadth)

Water Height = Volume of water ÷ Base Area

Example 2: Finding Water Level

A rectangular tank measures 40 cm by 25 cm by 60 cm. It is filled with 45 litres of water.

(a) What is the height of the water level?

Tank: 40 cm × 25 cm × 60 cm, filled with 45 litres

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Solution:

First, convert litres to cm³:

Volume of water = 45 litres = 45 × 1000 = 45,000 cm³

Height of water level = Volume ÷ (Length × Breadth)

$= \frac{45{,}000}{40 \times 25}$

$= \frac{45{,}000}{1000}$

= 45 cm

The height of the water level is 45 cm.

Example 3: Water Needed to Fill Tank

A rectangular tank measures 40 cm by 25 cm by 60 cm. It is filled with 45 litres of water.

(b) How much more water is needed to fill the tank completely? Give your answer in litres.

How much more water to fill completely?

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Method 1: Using Total Volume

Volume of tank = 40 × 25 × 60 = 60,000 cm³

60,000 cm³ = 60 litres

Volume of water needed = 60 − 45 = 15 litres

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Method 2: Using Empty Space

Height of tank not filled with water = 60 − 45 = 15 cm

Volume of water needed = 40 × 25 × 15 = 15,000 cm³

15,000 cm³ = 15 litres

15 litres more water is needed to fill the tank completely.

3. Multi-step and Transfer Problems

Problem Types

Fractional fill: Tank is $\frac{2}{3}$ filled with water
Pouring away: Water is removed from tank
Transfer: Water moved from one container to another
Rate problems: Water flows in at a given number of litres per minute

Example 4: Water Poured Away

A rectangular tank is 38 cm long, 24 cm wide and 20 cm high. The height of the water level in the tank is 15 cm. Mrs Loh pours away 5472 cm³ of water from the tank. What is the height of the remaining amount of water?

Before:

Initial water level: 15 cm

After pouring away 5472 cm³:

Remaining water level: ?

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Method 1: Find remaining volume first

Volume of water at first = 38 × 24 × 15 = 13,680 cm³

Volume of water left = 13,680 − 5472 = 8208 cm³

Height of remaining water = $\frac{8208}{38 \times 24} = \frac{8208}{912}$ = 9 cm

Method 2: Find decrease in height

Decrease in height of water level = $\frac{5472}{38 \times 24} = \frac{5472}{912}$ = 6 cm

Height of remaining water = 15 − 6 = 9 cm

The height of the remaining amount of water is 9 cm.

Example 5: Fractional Fill Problem

Tank A, which measures 48 cm by 18 cm by 40 cm, is $\frac{3}{4}$ filled with water. Ali pours all the water from Tank A into an empty cubical container. The height of the water level in the cubical container is 20 cm. Find the length of the edge of the cubical container.

Tank A: 3/4 filled

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Solution:

Height of water level in Tank A = $\frac{3}{4}$ × 40 = 30 cm

Volume of water in Tank A = 48 × 18 × 30 = 25,920 cm³

In the cubical container:

Base area of cubical container = Volume ÷ Height

$= \frac{25{,}920}{20}$ = 1296 cm²

Since it's a cube: Edge × Edge = 1296

Length of edge = $\sqrt{1296}$ = 36 cm

The length of the edge of the cubical container is 36 cm.

Example 6: Rate Problem

A rectangular tank with a base area of 9600 cm² and a height of 60 cm is half-filled with water. A tap is turned on and water flows into the tank at a rate of 32 litres per minute. How long does it take to fill the tank to the brim?

Base area = 9600 cm², height = 60 cm. The tank is half-filled. How long to fill it to the brim?

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Solution:

Tank is half-filled, so we need to fill the other half.

Volume of empty space = Base Area × $\frac{1}{2}$ × Height

= 9600 × $\frac{1}{2}$ × 60

= 9600 × 30

= 288,000 cm³

= 288 litres

Time to fill = Volume needed ÷ Rate

= 288 ÷ 32

= 9 minutes

It takes 9 minutes to fill the tank to the brim.

Problem-Solving Tips

For Water Level Problems

• Convert litres to cm³ first (×1000)
• Water height = Volume ÷ Base Area
• Base Area = Length × Breadth

For Transfer Problems

• Volume of water stays the same
• Calculate volume from first container
• Use that volume for second container

For Fractional Fill

• $\frac{3}{4}$ filled → water height = $\frac{3}{4}$ × total height
• Or: volume of water = $\frac{3}{4}$ × total volume

For Rate Problems

• Time = Volume ÷ Rate
• Match units (litres with litres/min)
• Convert cm³ to litres if needed

Key Takeaways

1.1 litre = 1000 cm³ (essential conversion)
2.Water height = Volume of water ÷ Base Area
3.Volume to fill = Total volume − Current water volume
4.When water is transferred, volume stays constant
5.Time = Volume ÷ Rate for flow problems
6.Always check your units match before calculating!