π/4 * d² (pi by 4 d square) represents the area of a circle where 'd' is the diameter of the circle.
Here's a breakdown:
- π (pi): A mathematical constant approximately equal to 3.14159. It represents the ratio of a circle's circumference to its diameter.
- d: Represents the diameter of the circle. The diameter is the distance across the circle passing through the center.
- d² (d squared): The diameter multiplied by itself (d * d).
- *π/4 d²:** The formula to calculate the area of a circle using its diameter.
Why πd²/4 calculates the Area:
The standard formula for the area of a circle is πr², where 'r' is the radius. The radius is half the diameter (r = d/2). Substituting d/2 for r in the area formula gives us:
Area = π (d/2)² = π (d²/4) = (π/4) * d²
Example:
If a circle has a diameter of 10 units, its area would be:
Area = (π/4) 10² = (3.14159/4) 100 ≈ 78.54 square units.
In summary, π/4 * d² is simply another way to express the area of a circle, specifically when the diameter is known.
