SAT Math: Arc Length and Sector Area
27+ practice questions in Praczo
The concept, explained
- 1
A sector is a slice of a circle. An arc is a piece of the circumference.
- 2
Proportion method: (Central Angle / 360°) = (Arc Length / Circumference) = (Sector Area / Total Area).
- 3
If the angle is in radians: Arc Length = rθ. Sector Area = (1/2)r²θ. (Where r is radius, θ is angle).
- 4
To convert degrees to radians, multiply by π/180. To convert radians to degrees, multiply by 180/π.
- 5
Often, the SAT gives you the arc length and asks for the circumference, or gives sector area and asks for the angle. Use the proportion.
- ✗ Using the area formula when asked for arc length, or vice versa.
- ✗ Using the radian formulas (s = rθ) when the angle is given in degrees.
SAT-style practice
In a circle with radius 6, what is the area of a sector with a central angle of 60°?
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