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Circles: Radians, arcs and sectors
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Measuring angles in radians, circumference & arc lengths and sector areas
Want a deeper conceptual understanding? Try our interactive lesson! (Plus Only)
Circumference & Area of a circle
SL AI 3.4
The ratio of a circle's perimeter to its diameter is constant in all circles. This constant is called π (pi). Since the diameter is twice the radius, the circumference of a circle is
C=2πr📖
The area of a circle is
A=πr2📖
where r is the radius of the circle.
Arc length (degrees)
SL AI 3.4
An arc is part of the circumference of a circle. It is defined by the radius r of the circle and the angle θ that the arc "sweeps out" over the circle's perimeter.
Since the arc length is a fraction of the overall circumference determined by the value of the angle θ, the arc length is calculated as
l=360∘θ×2πr
Sector (degrees)
SL AI 3.4
A sector is an area enclosed between a circular arc and the two radii of the circle touching each end of the arc, like a slice of pizza.
The area of a circle is πr2, and there are 360 degrees of rotation in a circle. Therefore, a sector with central angle θ is 360∘θ of a full circle, and has area
A=360∘θ×πr2
Nice work completing Circles: Radians, arcs and sectors, here's a quick recap of what we covered:
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