Fencing the round pond
You want to fence a circular pond and line its edge with lights. The fence length is the circumference (2πr) and the water surface is the area (πr²) — both come straight from the radius and the number π.
π ties a circle together
The radius r is the distance from a circle's center to its edge; the diameter d is twice the radius. The circumference (distance around) is C = 2πr, and the area (space inside) is A = πr². The constant π ≈ 3.14159 appears in both.
Don't confuse the two formulas
Circumference grows with r (2πr); area grows with r² (πr²). Doubling the radius doubles the circumference but quadruples the area.
A circle with r = 3: circumference = 2π·3 ≈ 18.85; area = π·3² = 9π ≈ 28.27.
Lab · Find the area
- A pizza has a radius of 5 inches.
- Apply A = πr².
- Compute the area (leave it in terms of π).
What you should see: A = π·5² = 25π ≈ 78.5 square inches.