Pi r squared (πr²) is the formula used to calculate the area of a circle. According to the reference, it represents the relationship between a circle's radius and its area.
Understanding Pi r Squared
Here's a breakdown:
- π (Pi): A mathematical constant, approximately 3.14159. It's the ratio of a circle's circumference to its diameter.
- r (radius): The distance from the center of the circle to any point on its edge.
- r² (radius squared): The radius multiplied by itself.
- πr² (Pi times radius squared): Multiplying pi by the square of the radius gives the area of the circle.
Formula Details
| Element | Description |
|---|---|
| π (Pi) | Constant ≈ 3.14159 |
| r | Radius of the circle |
| r² | Radius multiplied by itself |
| πr² | Area of the circle |
Practical Examples
Let's illustrate how πr² works in practice:
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Example 1: If a circle has a radius of 5 cm, its area is:
- π (5 cm)² = π 25 cm² ≈ 78.54 cm²
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Example 2: A circle with a radius of 10 meters has an area of:
- π (10 m)² = π 100 m² ≈ 314.16 m²
Significance of Pi r Squared
- Fundamental formula: It's a cornerstone of geometry, crucial for understanding circle properties.
- Real-world applications: It's utilized in fields like engineering, construction, and design to calculate the surface area of circular shapes, such as pipes, gears, and even pizza.
- Precision: The formula allows for accurate calculation of the area, aiding precision in designs and measurements.
In essence, pi r squared is not just an abstract formula, it's a fundamental tool for understanding and working with circles in numerous real-world situations.
