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How It Works
Every circle calculation starts with the radius. Area equals πr², circumference equals 2πr, and the diameter is simply twice the radius. For arcs and sectors, you also need the central angle θ (in radians): arc length is rθ and sector area is ½r²θ.
Example Problem
A circle has a radius of 5 cm. Find its area and circumference.
- Area = π × 5² = 25π ≈ 78.54 cm²
- Circumference = 2π × 5 = 10π ≈ 31.42 cm
Frequently Asked Questions
How to find the area of a circle from the diameter?
Divide the diameter by 2 to get the radius, then use A = πr². For a circle with diameter 10, the radius is 5, so the area is π × 25 ≈ 78.54 square units.
What is the difference between arc length and circumference?
Circumference is the total distance around the circle (2πr). Arc length is only a portion of that distance, determined by the central angle. A 90-degree arc is one-quarter of the full circumference.
How to calculate the area of a sector?
Use A = ½r²θ where θ is in radians. If the angle is in degrees, convert first by multiplying by π/180. A sector with radius 4 and angle 60° has area ½ × 16 × (π/3) ≈ 8.38 square units.
What is a circle segment?
A segment is the region between a chord and the arc it subtends. Its area equals the sector area minus the triangle area: A = ½r²(θ − sinθ).
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