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Area

Circle Area

Learn S = πr², annulus area, semicircle area, and how scaling radius affects area.

Core Formulas

Circle

S = πr²

Semicircle

S = ½πr²

Annulus (Ring)

S = π(R² − r²)

Examples

Given radius: r = 4 cm → S = πr² = 16π ≈ 50.24 cm²
Given diameter: d = 10 cm → r = 5 → S = 25π ≈ 78.5 cm²
Annulus (ring): R = 5, r = 2 → S = π(R² − r²) = π(25 − 4) = 21π

Scaling & Pitfalls

Scaling Rule

If r → kr, then S → k²S. Doubling radius quadruples area.

Common Pitfalls

• Using πd instead of πr² (confusing circumference with area).
• Forgetting to square the radius.
• Thinking doubling radius doubles area (it quadruples).

Practice & Tools

Circle Calculator

Compute area/circumference from radius/diameter.

Method: S = πr²; C = 2πr
Related: scaling S ∝ r², unit conversion

Annulus Calculator

Compute ring area from inner/outer radii.

Method: S = π(R² − r²)
Related: difference of areas, concentric circles

Practice

Apply area formulas to varied problems.