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The Humongous Book of Trigonometry Problems by W. Michael Kelley

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Area of a Sector

Surface area of a pizza slice

12.35 Identify the formula used to calculate the area of a sector with central angle θ.

A sector is a portion of a circle bounded by an arc and two radii of the circle. To compute the area of a sector, you need to know the measure of its central angle θ and the radius r of the circle.

The vertex of a central angle lies on the center of a circle and its sides extend outward from the center, intersecting the circle.

Essentially, this formula multiplies the area of the full circle by a fraction that ...

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