Explanation
The area of a circle means the amount of space inside the circle.
But why is the formula for the area of a circle:
\(A=\pi r^2 \)
To understand this, we can imagine cutting the circle into many equal slices, like pizza slices.
When these slices are rearranged, they begin to look like a rectangle.
The new rectangle has:
- Length \(=\) half of the circumference
- Width \(=\) radius
The circumference of a circle is:
\(C=2\pi r\)
So half of the circumference is:
\(\frac{1}{2}C=\frac{1}{2}(2\pi r)=\pi r\)
Therefore:
- Length \(= \pi r\)
- Width \(= r\)
Now use the area of a rectangle:
\(A = \text{length} \times \text{width}\)
So:
\(A=\pi r×r\)
\(A=\pi r^2\)
This is why the area of a circle is:
\(A=πr^2\)
Formula / Rule
Circumference of a Circle
\(C=2\pi r\)
Where:
- \(C = \) circumference
- \(r = \) radius
- \(\pi \approx 3.14 \)
Area of a Circle
\(A=\pi r^2\)
Where:
- \(A = \) area
- \(r = \) radius
Example
Find the area of a circle with radius:
\(r=3 \text{ m}\)
Use the formula:
\(A=\pi r^2\)
Substitute \(r = 3\):
\(A=\pi(3)^2\)
\(A=9π \text{ m}^2\)
Using \(\pi \approx 3.14 \):
\(A≈9(3.14)\)
\(A≈28.26 \text{ m}^2\)
So, the area of the circle is:
\(9\pi \text{ m}^2\)
or approximately:
\(28.26 \text{ m}^2\)
Video Explanation
Practice
Continue Learning
- What is \(\pi\) (pi)? An Easy Explanation
- Why the Area of a Circle is \(\pi r^2\) (Visual Explanation) (Current lesson)