ACT Preparation / Unit 14 ACT 1308 worked example, 60 to 90 seconds
Arc Length and Sector Area
The idea
Arc and sector problems are solved in three steps. First, find the central angle θ and the radius r. Second, form the fraction θ/360, or θ/2π if the angle is in radians. Third, multiply the circumference by the fraction for an arc length, or the area by the fraction for a sector, simplifying the fraction first. In radians, arc length is rθ and sector area is ½r²θ.
In practice
Worked example: a pizza of radius 9 inches is cut into slices with a central angle of 40°. Fraction: 40/360 = 1/9. Crust length of one slice: (1/9) × 18π = 2π, about 6.3 inches. Area of one slice: (1/9) × 81π = 9π, about 28.3 square inches.
Where people slip
Arc length is a length and sector area is an area. A question about the crust wants the arc; a question about the cheese wants the sector.
Your place on the trail
Every lesson rests on earlier ones and opens later ones. Tap any to jump.
Builds on
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