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=length×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:
\(r=3 m\)
Use the formula:
\(A=\pi r^2\)
Substitute \(r = 3\):
\(A=\pi(3)^2\)
\(A=9π m^2\)
Using \(\pi \approx 3.14 \):
\(A≈9(3.14)\)
\(A≈28.26 m^2\)
So, the area of the circle is:
\(9\pi m^2\)
or approximately:
\(28.26 m^2\)
Video Explanation
Practice
Continue Learning
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