Volume Word Problems (Grade 5)
Volume word problems ask you to apply the formulas for volume of cubes and cuboids to real-life situations. These problems involve water tanks, boxes, rooms, packing items, and other everyday objects.
In Class 5, solving volume word problems requires careful reading, identifying the correct formula, converting units when needed, and performing step-by-step calculations.
The key formulas used are:
- Volume of cuboid = Length × Breadth × Height
- Volume of cube = Side × Side × Side
- 1 m³ = 1,000 litres = 10,00,000 cm³
- 1 cm³ = 1 mL
What is Volume Word Problems - Class 5 Maths (Measurement)?
A volume word problem is a question where you must read a real-life scenario and calculate the volume (space inside) of a three-dimensional object. These problems may ask you to:
- Find the volume of a container or box
- Find how much liquid a tank can hold (capacity)
- Find a missing dimension when volume is given
- Compare volumes of two or more objects
- Calculate how many smaller objects fit inside a larger one
Volume Word Problems (Grade 5) Formula
Volume of Cuboid = l × b × h | Volume of Cube = s³
Useful Conversions:
| From | To | Multiply by |
|---|---|---|
| 1 m³ | litres | 1,000 |
| 1 m³ | cm³ | 10,00,000 |
| 1 litre | cm³ | 1,000 |
| 1 cm³ | mL | 1 |
Solved Examples
Example 1: Example 1: Water Tank Capacity
Problem: A rectangular water tank is 3 m long, 2 m wide, and 1.5 m deep. How many litres of water can it hold?
Solution:
Step 1: Volume = l × b × h = 3 × 2 × 1.5 = 9 m³
Step 2: Convert to litres: 9 × 1,000 = 9,000 litres
Answer: The tank can hold 9,000 litres of water.
Example 2: Example 2: Packing Boxes
Problem: Ria has a large box measuring 60 cm × 40 cm × 30 cm. She wants to pack small cubes of side 10 cm inside it. How many small cubes can fit?
Solution:
Step 1: Volume of large box = 60 × 40 × 30 = 72,000 cm³
Step 2: Volume of one small cube = 10 × 10 × 10 = 1,000 cm³
Step 3: Number of cubes = 72,000 ÷ 1,000 = 72
Answer: 72 small cubes can fit inside the box.
Example 3: Example 3: Finding Height of a Room
Problem: A room has a volume of 180 m³. Its length is 10 m and breadth is 6 m. Find the height of the room.
Solution:
Step 1: V = l × b × h, so h = V ÷ (l × b)
Step 2: h = 180 ÷ (10 × 6) = 180 ÷ 60 = 3
Answer: Height of the room = 3 m
Example 4: Example 4: Sand in a Pit
Problem: Aman's father dug a rectangular pit 4 m long, 3 m wide, and 2 m deep. How many cubic metres of sand are needed to fill it?
Solution:
Step 1: Volume = 4 × 3 × 2 = 24 m³
Answer: 24 m³ of sand is needed.
Example 5: Example 5: Comparing Containers
Problem: Container A is 50 cm × 30 cm × 20 cm. Container B is a cube with side 35 cm. Which container has more space?
Solution:
Step 1: Volume of A = 50 × 30 × 20 = 30,000 cm³
Step 2: Volume of B = 35 × 35 × 35 = 42,875 cm³
Step 3: Compare: 42,875 > 30,000
Answer: Container B has more space.
Example 6: Example 6: Filling a Tank with Buckets
Problem: Priya has a tank that holds 500 litres. She fills it using a bucket that holds 10 litres. How many buckets does she need?
Solution:
Step 1: Number of buckets = Total capacity ÷ Bucket capacity
Step 2: = 500 ÷ 10 = 50
Answer: Priya needs 50 buckets.
Example 7: Example 7: Volume of a Suitcase
Problem: Kavi's suitcase is 70 cm long, 45 cm wide, and 25 cm deep. What is its volume in litres? (1 litre = 1,000 cm³)
Solution:
Step 1: Volume = 70 × 45 × 25 = 78,750 cm³
Step 2: Convert to litres: 78,750 ÷ 1,000 = 78.75 litres
Answer: Volume = 78.75 litres
Example 8: Example 8: Soil for a Garden Bed
Problem: A rectangular garden bed is 2.5 m long, 1.2 m wide, and 0.4 m deep. How many cubic metres of soil are needed to fill it?
Solution:
Step 1: Volume = 2.5 × 1.2 × 0.4
Step 2: 2.5 × 1.2 = 3.0, then 3.0 × 0.4 = 1.2
Answer: 1.2 m³ of soil is needed.
Example 9: Example 9: Half-Filled Tank
Problem: A cuboidal tank is 80 cm long, 60 cm wide, and 50 cm high. It is half filled with water. How many cm³ of water are in the tank?
Solution:
Step 1: Full volume = 80 × 60 × 50 = 2,40,000 cm³
Step 2: Half volume = 2,40,000 ÷ 2 = 1,20,000 cm³
Answer: The tank contains 1,20,000 cm³ of water.
Example 10: Example 10: Bricks in a Wall
Problem: Each brick is 20 cm × 10 cm × 8 cm. A wall has volume 16,000 cm³. How many bricks are needed?
Solution:
Step 1: Volume of one brick = 20 × 10 × 8 = 1,600 cm³
Step 2: Number of bricks = 16,000 ÷ 1,600 = 10
Answer: 10 bricks are needed.
Key Points to Remember
- Read the problem carefully to identify the shape (cube or cuboid).
- Write down the given values and what you need to find.
- Convert all measurements to the same unit before calculating.
- Use V = l × b × h for cuboids and V = s³ for cubes.
- Remember: 1 m³ = 1,000 litres and 1 litre = 1,000 cm³.
- For "how many fit inside" problems, divide the larger volume by the smaller volume.
- For missing dimension problems, divide the volume by the product of the known dimensions.
Practice Problems
- A fish tank is 50 cm long, 30 cm wide, and 35 cm tall. How many litres of water can it hold?
- Aditi wants to fill a cubic container of side 20 cm with sugar cubes of side 2 cm. How many sugar cubes are needed?
- A swimming pool is 20 m long, 8 m wide, and 2 m deep. How many litres of water does it need to be completely filled?
- A box has volume 4,800 cm³. Its length is 20 cm and breadth is 16 cm. Find the height.
- Dev has two containers: a cuboid (40 cm × 25 cm × 20 cm) and a cube (30 cm side). Which holds more?
- A rectangular pit measuring 5 m × 3 m × 2 m is to be filled with earth. If a truck carries 6 m³ per trip, how many trips are needed?
- Neha pours 15 litres of water into a tank measuring 50 cm × 30 cm × 20 cm. Will the tank overflow?
- A room is 8 m long, 5 m wide, and 3 m high. Find the volume of air in the room.
Frequently Asked Questions
Q1. How do you solve volume word problems?
Read the problem carefully, identify the shape (cube or cuboid), note the given measurements, convert to the same units if needed, apply the correct formula, and write the answer with proper units.
Q2. What is the difference between volume and capacity in word problems?
Volume refers to the space a solid takes up. Capacity refers to how much liquid a container can hold. In word problems about tanks, both terms mean the same thing — the internal space of the container.
Q3. How do you convert cubic metres to litres?
Multiply by 1,000. So 5 m³ = 5 × 1,000 = 5,000 litres. This is important for water tank and pool problems.
Q4. How do you find how many small boxes fit in a large box?
Calculate the volume of the large box and the small box separately. Then divide: Number of small boxes = Volume of large box ÷ Volume of one small box.
Q5. What if the tank is only partly filled?
Calculate the full volume first, then multiply by the fraction that is filled. For a half-filled tank, divide the full volume by 2. For a quarter-filled tank, divide by 4.
Q6. Why is unit conversion important in volume problems?
All three dimensions must be in the same unit before multiplying. Mixing metres and centimetres gives wrong answers. Convert all to one unit first.
Q7. How do you find a missing dimension from volume?
Use the formula: Missing dimension = Volume ÷ (product of the other two dimensions). For example, if V = 600, l = 10, b = 12, then h = 600 ÷ (10 × 12) = 5.
Q8. What does cubic centimetre (cm³) mean?
1 cm³ is the volume of a tiny cube with each side measuring 1 cm. It equals 1 millilitre (mL) of liquid.
