Volume Word Problems
Apply your volume knowledge to solve real-world problems
1. Finding Volume of Water in a Tank
Strategy:
Use the formula: Volume of water = length × breadth × water height
Note: The water height is how high the water is in the tank (not the tank's total height).
Example: Volume of Water in a Tank
A cubical tank of side 30 cm is partially filled with water. The height of the water level is 12 cm. What is the volume of water in the tank?
Solution:
Volume of water = length × breadth × water height
= 30 cm × 30 cm × 12 cm
Volume of water = 10,800 cm³
2. Finding Water Needed to Fill a Tank
Two Methods:
Method 1:
Water needed = Total volume − Current water volume
Method 2:
Find the empty height, then: Water needed = length × breadth × empty height
Example: Water Needed to Fill Tank
A cubical tank of side 30 cm has water to a height of 12 cm. How much more water is needed to fill the tank completely?
Solution (Method 2):
Height of tank not filled with water = 30 cm − 12 cm = 18 cm
Volume of water needed = 30 cm × 30 cm × 18 cm
= 16,200 cm³
3. Water Transfer Problems
Strategy:
- Find the volume of water in Container A
- Find the volume of Container B (or how much water fills it)
- Calculate: Water left = Water in A − Water transferred to B
Example: Pouring Water Between Containers
Cubical container A of side 35 cm was filled with water to a height of 16 cm. Some of the water was poured into an empty rectangular container B (40 cm × 15 cm × 12 cm) to fill it to the brim. Find the volume of water left in container A. Give your answer in litres and millilitres.
Solution:
Step 1: Volume of water in container A
= 35 × 35 × 16 = 19,600 cm³
Step 2: Volume of container B (water transferred)
= 40 × 15 × 12 = 7,200 cm³
Step 3: Volume of water left in A
= 19,600 − 7,200 = 12,400 cm³
= 12,400 ml = 12 ℓ 400 ml
Water left in A = 12 ℓ 400 ml
4. Fractional Fill Problems
Understanding Fractional Fill:
When a rectangular tank is "²⁄₃ full", it means the water height is ²⁄₃ of the tank's total height.
Water height = fraction × total height
Example: If an 18 cm tall tank is ²⁄₃ full, water height = ²⁄₃ × 18 = 12 cm
Example: Tank ²⁄₃ Full
A rectangular tank measuring 32 cm by 32 cm by 18 cm contained 3 ℓ of water at first. Some water was poured into the tank until it was ²⁄₃ full. How much water was added into the tank?
Solution:
Step 1: Find water height when ²⁄₃ full
Water height = ²⁄₃ × 18 cm = 12 cm
Step 2: Find volume when ²⁄₃ full
= 32 × 32 × 12 = 12,288 cm³ = 12,288 ml
Step 3: Convert initial water to ml
3 ℓ = 3,000 ml = 3,000 cm³
Step 4: Find water added
= 12,288 − 3,000 = 9,288 cm³
Water added = 9,288 cm³ (or 9,288 ml)
Example: Bottles into Tank
6 bottles of water were emptied into an empty rectangular tank measuring 24 cm by 20 cm by 15 cm until the tank was ⁴⁄₅ full of water. Each bottle contained the same amount of water. How much water was in each bottle?
Solution:
Step 1: Find water height when ⁴⁄₅ full
Water height = ⁴⁄₅ × 15 cm = 12 cm
Step 2: Find total volume of water
= 24 × 20 × 12 = 5,760 cm³
Step 3: Find volume in each bottle
= 5,760 ÷ 6 = 960 cm³
Each bottle = 960 cm³ (or 960 ml)
Practice Problems
Practice 1: Volume of Water
A rectangular tank is 36 cm long, 20 cm wide and 24 cm high. It is filled with water to a depth of 13 cm. Find the volume of water in the tank.
ShowHide solution
Volume = 36 × 20 × 13
= 9,360 cm³
Practice 2: Water Needed
A rectangular tank is 36 cm long, 20 cm wide and 24 cm high. It is filled with water to a depth of 13 cm. Find the volume of water needed to fill the tank completely.
ShowHide solution
Empty height = 24 − 13 = 11 cm
Water needed = 36 × 20 × 11
= 7,920 cm³
Practice 3: Using Jugs to Fill
A rectangular tank 40 cm long, 15 cm wide and 20 cm high is partially filled with water to a height of 8 cm. The capacity of a jug is 800 ml. How many jugs of water are needed to fill the tank to its brim?
ShowHide solution
Empty height = 20 − 8 = 12 cm
Water needed = 40 × 15 × 12 = 7,200 cm³ = 7,200 ml
Number of jugs = 7,200 ÷ 800 = 9 jugs
Practice 4: Fractional Fill
A rectangular tank measuring 18 cm by 10 cm by 12 cm was ⁵⁄₆ full of water at first. 440 cm³ of the water was poured away. What was the volume of water left? Express your answer in millilitres.
ShowHide solution
Water height = ⁵⁄₆ × 12 = 10 cm
Initial volume = 18 × 10 × 10 = 1,800 cm³
Water left = 1,800 − 440 = 1,360 cm³
= 1,360 ml
Practice 5: Challenge Problem
A rectangular tank has a square base with sides 9 m and height of 11 m. It contained 250 m³ of water. Another 425 m³ was poured into the tank. How much more water is needed to fill the tank completely?
ShowHide solution
Total tank volume = 9 × 9 × 11 = 891 m³
Current water = 250 + 425 = 675 m³
Water needed = 891 − 675 = 216 m³
Key Takeaways
- Volume of water = length × breadth × water height
- Water needed to fill = Total volume − Current water volume
- Or: Water needed = length × breadth × empty height
- For fractional fill: Water height = fraction × total height
- In transfer problems: Water left = Initial water − Water transferred
- Always convert to the required units (ml, ℓ, cm³, m³)