Explanation
Length, area, and volume are important ideas in mathematics that help us measure objects in different dimensions.
Length measures the distance between two points.
Area measures the space inside a flat (2D) shape.
Volume measures the space inside a 3D object.
We can also think about them using dimensions:
1D (One-Dimensional) → Length only
2D (Two-Dimensional) → Length and width
3D (Three-Dimensional) → Length, width, and height
For example:
A line segment is 1D.
A square is 2D.
A cube is 3D.
Area is made from many line segments, and volume is made from many layers of area.
Formula / Rule
📏 Length
Length measures the distance between two points.
Example unit:
meters (m)
🟦 Area
Area measures how many square units cover a flat shape.
For a rectangle or square:
A=L×W
Example units:
square meters (m²)
square centimeters (cm²)
🧊 Volume
Volume measures how many cubes fill a 3D object.
For a rectangular prism or cube:
V=L×W×H
Example units:
cubic meters (m³)
cubic centimeters (cm³)
Example
Example 1 — Length
A line segment has length 3 m.
So, the distance from one point to the other point is:
Length = 3 m
Example 2 — Area
A square has:
Length = 3 m
Width = 3 m
Using the area formula:
A=L×W=3×3=9 m²
So, the area is:
9 square meters
This means 9 small squares of size 1 m×1 m can fill the square.
Example 3 — Volume
A cube has:
Length = 3 m
Width = 3 m
Height = 3 m
Using the volume formula:
V=L×W×H=3×3×3=27 m³
So, the volume is:
27 cubic meters
This means 27 small cubes of size 1 m×1 m×1 m can fill the cube.
Video Explanation
Practice
Continue Learning
- Length, Area, and Volume: What’s the Difference?
- Why the Area of a Circle is 𝜋𝑟2 (Visual Explanation)