Volume of Cubes and Cuboids
Learn the formulas to calculate volume without counting every cube
1. Volume Formula for Cuboids
The Big Idea:
Instead of counting every cube, we can use a formula to calculate volume quickly!
Understanding the Formula:
A cuboid has 3 dimensions:
- • Length - how long it is
- • Breadth - how wide it is
- • Height - how tall it is
Volume Formula for Cuboid
Volume = length × breadth × height
or V = L × B × H
Why does this work? The formula counts all the cubes at once:
- • Length × Breadth = cubes in one layer
- • × Height = total cubes (all layers)
Example: Volume of a Cuboid
A cuboid measures 4 cm by 2 cm by 3 cm. Find its volume.
Solution:
Volume = length × breadth × height
Volume = 4 cm × 2 cm × 3 cm
Volume = 24 cm³
2. Volume Formula for Cubes
What makes a cube special?
A cube is a special cuboid where all edges are the same length.
All edges of a cube are equal!
Volume Formula for Cube
Volume = length × length × length
or V = L × L × L
Example: Volume of a Cube
A cube has edges of 2 cm. Find its volume.
Solution:
Volume = length × length × length
Volume = 2 cm × 2 cm × 2 cm
Volume = 8 cm³
3. Applying the Formulas
Steps to Find Volume:
- Identify the shape (cube or cuboid)
- Find the dimensions (length, breadth, height)
- Use the correct formula
- Calculate and include the correct unit (cm³ or m³)
Example: Finding Volume of a Room
A room measures 12 m by 8 m by 4 m. Find its volume.
Solution:
Volume = length × breadth × height
Volume = 12 m × 8 m × 4 m
Volume = 384 m³
Example: Finding Volume of a Container
A rectangular glass container measures 10 cm by 6 cm by 4 cm. What is its volume?
Solution:
Volume = length × breadth × height
Volume = 10 cm × 6 cm × 4 cm
Volume = 240 cm³
Practice Problems
Practice 1: Volume of a Cuboid
A cuboid measures 5 cm by 3 cm by 2 cm. Find its volume.
ShowHide solution
Volume = 5 × 3 × 2
Volume = 30 cm³
Practice 2: Volume of a Cube
Find the volume of a cube with edges of 6 cm.
ShowHide solution
Volume = 6 × 6 × 6
Volume = 216 cm³
Practice 3: Volume in m³
A storage container measures 10 m by 5 m by 12 m. Find its volume.
ShowHide solution
Volume = 10 × 5 × 12
Volume = 600 m³
Practice 4: Volume of a Cube (m³)
A cubical water tank has edges of 4 m. What is its volume?
ShowHide solution
Volume = 4 × 4 × 4
Volume = 64 m³
Key Takeaways
- Volume of cuboid = length × breadth × height
- Volume of cube = length × length × length
- A cube is a special cuboid with all edges equal
- Always include the correct unit: cm³ or m³
- The formula counts all the cubes at once using multiplication