Volume of Cuboid
A cuboid is a three-dimensional shape with six rectangular faces. Boxes, bricks, books, and tiffin boxes are all cuboids. The volume of a cuboid tells us how much space is inside it.
In Class 5 Maths, you learn to calculate the volume of a cuboid using its three measurements: length, breadth (or width), and height. Volume is measured in cubic units such as cm³, m³, or mm³.
Understanding volume helps in real-life tasks like finding how much water a tank can hold, how many items fit inside a box, or how much soil is needed to fill a flower bed.
What is Volume of Cuboid - Class 5 Maths (Measurement)?
The volume of a cuboid is the total space enclosed within its six rectangular faces. It is the product of its length, breadth, and height.
A cuboid has:
- Length (l) — the longest side along the base
- Breadth (b) — the shorter side along the base (also called width)
- Height (h) — the vertical measurement from base to top
All measurements must be in the same unit before calculating volume.
Volume of Cuboid Formula
Volume of Cuboid = Length × Breadth × Height
V = l × b × h
The answer is always in cubic units:
| If measurements are in | Volume is in |
|---|---|
| centimetres (cm) | cubic centimetres (cm³) |
| metres (m) | cubic metres (m³) |
| millimetres (mm) | cubic millimetres (mm³) |
Finding a Missing Dimension:
- Length = Volume ÷ (Breadth × Height)
- Breadth = Volume ÷ (Length × Height)
- Height = Volume ÷ (Length × Breadth)
Types and Properties
Special Cases of Cuboids
- Cube: When length = breadth = height, the cuboid becomes a cube. Volume = side × side × side = side³.
- Flat cuboid: When the height is very small compared to length and breadth (like a book or a tile).
- Tall cuboid: When the height is much larger than length and breadth (like a pillar or a tall box).
Solved Examples
Example 1: Example 1: Basic Volume Calculation
Problem: Find the volume of a cuboid with length 8 cm, breadth 5 cm, and height 3 cm.
Solution:
Step 1: Write the formula: V = l × b × h
Step 2: Substitute the values: V = 8 × 5 × 3
Step 3: Calculate: V = 120
Answer: Volume = 120 cm³
Example 2: Example 2: Volume of a Brick
Problem: A brick is 20 cm long, 10 cm wide, and 8 cm high. Calculate its volume.
Solution:
Step 1: V = l × b × h
Step 2: V = 20 × 10 × 8
Step 3: V = 1600
Answer: Volume of the brick = 1,600 cm³
Example 3: Example 3: Tiffin Box Problem
Problem: Ria's tiffin box is 15 cm long, 12 cm wide, and 6 cm tall. How much space is inside the tiffin box?
Solution:
Step 1: V = l × b × h
Step 2: V = 15 × 12 × 6
Step 3: V = 1080
Answer: The tiffin box has a volume of 1,080 cm³.
Example 4: Example 4: Volume in Metres
Problem: A room is 5 m long, 4 m wide, and 3 m high. Find the volume of the room.
Solution:
Step 1: V = l × b × h
Step 2: V = 5 × 4 × 3
Step 3: V = 60
Answer: Volume of the room = 60 m³
Example 5: Example 5: Finding the Missing Height
Problem: A cuboid has a volume of 360 cm³, length 10 cm, and breadth 6 cm. Find the height.
Solution:
Step 1: V = l × b × h, so h = V ÷ (l × b)
Step 2: h = 360 ÷ (10 × 6)
Step 3: h = 360 ÷ 60 = 6
Answer: Height = 6 cm
Example 6: Example 6: Water Tank Problem
Problem: Aman's father has a rectangular water tank that is 2 m long, 1 m wide, and 1 m high. How many litres of water can it hold? (1 m³ = 1000 litres)
Solution:
Step 1: V = l × b × h = 2 × 1 × 1 = 2 m³
Step 2: Convert to litres: 2 × 1000 = 2000 litres
Answer: The tank can hold 2,000 litres of water.
Example 7: Example 7: Comparing Two Boxes
Problem: Box A is 10 cm × 8 cm × 5 cm. Box B is 12 cm × 6 cm × 7 cm. Which box has a greater volume?
Solution:
Step 1: Volume of Box A = 10 × 8 × 5 = 400 cm³
Step 2: Volume of Box B = 12 × 6 × 7 = 504 cm³
Step 3: Compare: 504 > 400
Answer: Box B has the greater volume.
Example 8: Example 8: Finding Breadth
Problem: Priya's pencil box has a volume of 480 cm³. It is 16 cm long and 5 cm high. Find the breadth.
Solution:
Step 1: b = V ÷ (l × h)
Step 2: b = 480 ÷ (16 × 5)
Step 3: b = 480 ÷ 80 = 6
Answer: Breadth = 6 cm
Example 9: Example 9: Stacking Cuboids
Problem: Kavi stacks 4 identical boxes. Each box is 30 cm long, 20 cm wide, and 10 cm tall. Find the total volume of all 4 boxes.
Solution:
Step 1: Volume of one box = 30 × 20 × 10 = 6,000 cm³
Step 2: Total volume = 4 × 6,000 = 24,000 cm³
Answer: Total volume = 24,000 cm³
Example 10: Example 10: Unit Conversion Before Calculation
Problem: A box is 1.5 m long, 80 cm wide, and 60 cm high. Find its volume in cm³.
Solution:
Step 1: Convert length to cm: 1.5 m = 150 cm
Step 2: V = 150 × 80 × 60
Step 3: V = 7,20,000
Answer: Volume = 7,20,000 cm³
Real-World Applications
Real-Life Uses of Volume of Cuboid
- Packing: Calculating how many items fit inside a box or carton.
- Construction: Finding the amount of concrete or soil needed to fill a rectangular pit.
- Water storage: Determining the capacity of rectangular tanks and containers.
- Shipping: Measuring cargo space in trucks and containers.
- Cooking: Knowing the capacity of rectangular baking trays and moulds.
Key Points to Remember
- A cuboid has 6 rectangular faces, 12 edges, and 8 vertices.
- Volume of cuboid = Length × Breadth × Height.
- Volume is measured in cubic units (cm³, m³, mm³).
- All three measurements must be in the same unit before multiplying.
- To find a missing dimension, divide the volume by the product of the other two dimensions.
- 1 m³ = 10,00,000 cm³ and 1 m³ = 1000 litres.
- A cube is a special cuboid where all sides are equal.
Practice Problems
- Find the volume of a cuboid with length 12 cm, breadth 7 cm, and height 4 cm.
- A chocolate box is 25 cm long, 15 cm wide, and 8 cm tall. What is its volume?
- Aditi's fish tank is 40 cm long, 20 cm wide, and 25 cm high. How much water (in cm³) can it hold?
- A cuboid has a volume of 600 cm³. Its length is 15 cm and height is 8 cm. Find the breadth.
- A storage container is 3 m long, 2 m wide, and 2 m high. How many litres of grain can it store? (1 m³ = 1000 litres)
- Dev has two boxes: Box P (9 cm × 6 cm × 4 cm) and Box Q (8 cm × 5 cm × 6 cm). Which box has the larger volume?
- A swimming pool is 25 m long, 10 m wide, and 2 m deep. Calculate its volume in m³.
- A cuboid has equal length and breadth of 7 cm each, and height 10 cm. Find the volume.
Frequently Asked Questions
Q1. What is the formula for the volume of a cuboid?
Volume of a cuboid = Length × Breadth × Height (V = l × b × h). The answer is always in cubic units such as cm³ or m³.
Q2. What is the difference between volume and capacity?
Volume is the total space a solid object occupies, while capacity is the amount of liquid a hollow container can hold. For a hollow cuboid like a water tank, volume and capacity refer to the same measurement.
Q3. Why must all dimensions be in the same unit?
If the dimensions are in different units (for example, metres and centimetres), the multiplication gives an incorrect answer. Always convert all measurements to the same unit before calculating.
Q4. How do you find the height of a cuboid if the volume is given?
Divide the volume by the product of length and breadth: Height = Volume ÷ (Length × Breadth). The same method works for finding any missing dimension.
Q5. What is the unit of volume?
Volume is measured in cubic units. If the dimensions are in centimetres, the volume is in cm³ (cubic centimetres). If in metres, the volume is in m³ (cubic metres).
Q6. How is a cuboid different from a cube?
A cuboid has three different measurements (length, breadth, height), while a cube has all three measurements equal. Every cube is a cuboid, but not every cuboid is a cube.
Q7. How many litres is 1 cubic metre?
1 cubic metre (m³) equals 1,000 litres. This conversion is useful when calculating the capacity of water tanks and swimming pools.
Q8. Is volume the same as area?
No. Area measures the surface of a flat shape in square units (cm², m²). Volume measures the space inside a three-dimensional shape in cubic units (cm³, m³). Volume needs one extra dimension.
Q9. What are some real-life examples of cuboids?
Books, bricks, tiffin boxes, refrigerators, rooms, shoe boxes, and erasers are all examples of cuboid shapes found in everyday life.
