Overview of Circle Area
The area of a circle refers to the space contained within its boundary.
Understanding Circle Area Through Visualization
If you divide a circle into numerous small segments and rearrange them, they will form a shape resembling a rectangle. This approach allows us to calculate the area of a circle similarly to how we calculate the area of a rectangle.
Steps to Calculate the Area
By dividing a circle into several segments and arranging them, the shape gradually becomes more rectangular. For instance, if you divide the circle into 8 parts and rearrange them, the resulting figure will resemble a rectangle. As the number of segments increases—16, 32, 64, and so on—the shape becomes increasingly closer to a rectangle.
Eventually, if the circle is divided into an infinite number of small pieces, a perfect rectangle is formed. The width of this rectangle corresponds to the circle's radius, while the length equals half the circle's circumference.
Formula for the Area of a Circle
Since the area of a rectangle is calculated by multiplying its width by its height, we can apply the same logic to the circle. The width of the 'rectangle' formed by the divided circle is the radius, and the height is half of the circle's circumference. The circumference of a circle is calculated as 2 × Ï€ × radius, so the area becomes:
Area of a Circle = Ï€ × radius²
Example: Circle vs. Square
Which is larger, a circular table with a diameter of 2 meters or a square table with a side length of 2 meters? Let’s calculate:
Circular Table
The radius of the circle is 1 meter. Using the formula for the area of a circle:
Area = 1 × 1 × 3.14 = 3.14 square meters.
Square Table
The area of a square is calculated as side × side, so the area of the square table is:
Area = 2 × 2 = 4 square meters.
Therefore, the square table is larger. If you compare the two shapes by drawing a circle inside the square, it becomes clear that the square covers more area than the circle.
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