Introduction to Volume
Volume is the amount of space a 3D object occupies. While area measures how much surface a flat shape covers, volume measures how much space a solid fills up.
In Class 5, you will learn what volume means, how to measure it using cubic units, how to count unit cubes, and how to calculate the volume of a cuboid using a formula.
What is Introduction to Volume - Class 5 Maths (Measurement)?
Volume is the measure of the space inside a 3D (three-dimensional) object.
Volume is measured in cubic units. One cubic centimetre (1 cm³) is the space occupied by a cube with side 1 cm.
Volume of Cuboid = Length × Breadth × Height
Volume of Cube = Side × Side × Side = Side³
Introduction to Volume Formula
Volume Formulas:
| Shape | Formula |
|---|---|
| Cuboid | l × b × h |
| Cube | s × s × s = s³ |
Unit conversions:
- 1 cm³ = 1 mL (millilitre)
- 1,000 cm³ = 1 litre
- 1 m³ = 1,000,000 cm³ = 1,000 litres
Capacity vs Volume: Volume is how much space an object takes up. Capacity is how much liquid a container can hold. They use the same measurement (1 cm³ = 1 mL).
Types and Properties
Methods to Find Volume:
- Counting unit cubes: Build or imagine the shape using 1 cm × 1 cm × 1 cm cubes. Count the total number of cubes.
- Using the formula: For cuboids, multiply length × breadth × height.
- Water displacement: For irregular shapes, submerge the object in water. The rise in water level (in cm³ or mL) equals the volume.
Understanding cubic units:
Area uses square units (2D: length × width). Volume uses cubic units (3D: length × width × height). The word "cubic" means three dimensions are multiplied.
Solved Examples
Example 1: Example 1: Volume of a Cuboid
Problem: Find the volume of a cuboid with length 8 cm, breadth 5 cm, and height 3 cm.
Solution:
Step 1: Volume = l × b × h
Step 2: Volume = 8 × 5 × 3 = 120 cm³
Answer: The volume is 120 cm³.
Example 2: Example 2: Volume of a Cube
Problem: Find the volume of a cube with side 6 cm.
Solution:
Step 1: Volume = Side × Side × Side
Step 2: Volume = 6 × 6 × 6 = 216 cm³
Answer: The volume is 216 cm³.
Example 3: Example 3: Counting Unit Cubes
Problem: A structure is built with unit cubes (1 cm each). It is 4 cubes long, 3 cubes wide, and 2 cubes high. What is the volume?
Solution:
Step 1: Total cubes = 4 × 3 × 2 = 24
Step 2: Each cube = 1 cm³, so volume = 24 cm³
Answer: The volume is 24 cm³.
Example 4: Example 4: Finding a Missing Dimension
Problem: A cuboid has volume 180 cm³, length 10 cm, and breadth 6 cm. Find the height.
Solution:
Step 1: Volume = l × b × h
Step 2: 180 = 10 × 6 × h
Step 3: 180 = 60 × h
Step 4: h = 180 ÷ 60 = 3 cm
Answer: The height is 3 cm.
Example 5: Example 5: Volume of a Tank
Problem: Rahul’s fish tank is 50 cm long, 30 cm wide, and 25 cm high. How many litres of water can it hold?
Solution:
Step 1: Volume = 50 × 30 × 25 = 37,500 cm³
Step 2: 1,000 cm³ = 1 litre
Step 3: 37,500 ÷ 1,000 = 37.5 litres
Answer: The tank holds 37.5 litres.
Example 6: Example 6: Volume of a Tiffin Box
Problem: Meera’s tiffin box is 18 cm long, 12 cm wide, and 6 cm high. Find its volume.
Solution:
Step 1: Volume = 18 × 12 × 6 = 1,296 cm³
Answer: The volume is 1,296 cm³.
Example 7: Example 7: Comparing Volumes
Problem: Box A is 10 cm × 8 cm × 5 cm. Box B is 12 cm × 6 cm × 6 cm. Which box has more volume?
Solution:
Step 1: Volume of A = 10 × 8 × 5 = 400 cm³
Step 2: Volume of B = 12 × 6 × 6 = 432 cm³
Step 3: 432 > 400
Answer: Box B has more volume (by 32 cm³).
Example 8: Example 8: Volume and Capacity
Problem: A container holds exactly 2 litres of water. Express its capacity in cm³.
Solution:
Step 1: 1 litre = 1,000 cm³
Step 2: 2 litres = 2 × 1,000 = 2,000 cm³
Answer: The capacity is 2,000 cm³.
Example 9: Example 9: Filling a Box with Cubes
Problem: How many 2 cm cubes can fit inside a box that is 10 cm × 8 cm × 6 cm?
Solution:
Step 1: Along the length: 10 ÷ 2 = 5 cubes.
Step 2: Along the breadth: 8 ÷ 2 = 4 cubes.
Step 3: Along the height: 6 ÷ 2 = 3 cubes.
Step 4: Total cubes = 5 × 4 × 3 = 60
Answer: 60 cubes of side 2 cm can fit inside the box.
Example 10: Example 10: Room Volume
Problem: A classroom is 10 m long, 8 m wide, and 3 m high. Find the volume of air in the room.
Solution:
Step 1: Volume = 10 × 8 × 3 = 240 m³
Answer: The volume is 240 m³.
Real-World Applications
Where do we use volume?
- Packing: How many items can fit inside a box or a container.
- Cooking: Measuring liquids — 250 mL cup, 1 litre bottle.
- Construction: How much concrete is needed to fill a pillar or foundation.
- Water storage: Finding how much water a tank or swimming pool can hold.
- Science: Measuring the volume of irregular objects by water displacement.
Key Points to Remember
- Volume measures the space inside a 3D shape.
- Volume is measured in cubic units (cm³, m³).
- Cuboid volume = length × breadth × height.
- Cube volume = side × side × side = side³.
- 1 cm³ = 1 mL. 1,000 cm³ = 1 litre.
- Capacity is the volume of liquid a container can hold.
- Volume is 3-dimensional (three measurements multiplied), unlike area (2D) or perimeter (1D).
- To find a missing dimension, divide the volume by the product of the other two dimensions.
Practice Problems
- Find the volume of a cuboid with length 15 cm, breadth 10 cm, and height 4 cm.
- A cube has a side of 9 cm. Find its volume.
- A cuboid has volume 360 cm³, length 12 cm, and breadth 6 cm. Find the height.
- A water tank is 2 m long, 1.5 m wide, and 1 m high. How many litres of water can it hold?
- How many 1 cm cubes can fit inside a box that is 5 cm × 4 cm × 3 cm?
- Neha has two boxes. Box P: 8 cm × 6 cm × 5 cm. Box Q: 10 cm × 5 cm × 4 cm. Which has greater volume?
- A cube-shaped ice block has volume 125 cm³. Find the side length.
- Convert 5 litres to cm³.
Frequently Asked Questions
Q1. What is volume?
Volume is the amount of space a 3D object occupies. It is measured in cubic units like cm³ or m³.
Q2. What is the formula for the volume of a cuboid?
Volume of a cuboid = length × breadth × height. All three measurements must be in the same unit.
Q3. What is the difference between area and volume?
Area measures the flat surface inside a 2D shape (in square units). Volume measures the space inside a 3D object (in cubic units). Area uses two dimensions; volume uses three.
Q4. What are cubic units?
Cubic units measure volume. 1 cm³ is the space occupied by a cube with edges of 1 cm. Common cubic units are cm³, m³, and km³.
Q5. How do you find the volume by counting cubes?
Count the number of unit cubes (1 cm × 1 cm × 1 cm) that fill the shape. The total count equals the volume in cm³.
Q6. What is the difference between volume and capacity?
Volume is the space an object takes up. Capacity is the amount of liquid a container can hold. Numerically they are the same (1 cm³ = 1 mL), but volume applies to solids too.
Q7. How many cm cubed are in 1 litre?
1 litre = 1,000 cm³. So 1 mL = 1 cm³.
Q8. How do I find the side of a cube if the volume is known?
Find the cube root of the volume. For example, if volume = 64 cm³, then side = cube root of 64 = 4 cm (since 4 × 4 × 4 = 64).
Q9. Can two different shaped boxes have the same volume?
Yes. For example, a 10×5×4 box and a 8×5×5 box both have volume 200 cm³ but look different.
Q10. Is this topic in the NCERT Class 5 syllabus?
Yes. Introduction to volume, cubic units, and the volume of cuboids and cubes are part of the Measurement chapter in NCERT/CBSE Class 5 Maths.
