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Sector Of A Circle

A sector of a circle is the region enclosed by two radii and the corresponding arc connecting their endpoints. It resembles a slice of pizza or pie cut from the center of the circle. The sector with the smaller arc is called the minor sector, while the one with the larger arc is the major sector.

Key Concepts

The angle formed by the two radii at the center of the circle is known as the central angle, which determines the size of the sector.
A circle is typically divided into a minor sector and a major sector, where the sum of their central angles is always 360 degrees.
The area of a sector is a proportional fraction of the total area of the circle, calculated based on the ratio of its central angle to 360 degrees.

Formula & Equation

Areaofasector=θ360∘×πr2Area of a sector = \frac{\theta}{360^\circ} \times \pi r^2

\theta is the central angle in degrees, r is the radius of the circle, and \pi is a mathematical constant approximately equal to \frac{22}{7} or 3.14.

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Common Misconceptions

Myth: Students often confuse a sector with a segment of a circle.
Fact: A sector is bounded by two radii and an arc, resembling a pizza slice, whereas a segment is bounded by a chord and an arc, resembling a piece cut straight off the edge of a circular cookie.

Real World Applications

A slice of a round pizza cut from the center to the crust perfectly represents a sector of a circle.
The area swept by the windshield wiper of a car forms a sector as it pivots around a fixed point.

Frequently Asked Questions

How do you find the area of a sector of a circle?
To find the area, divide the central angle by 360 degrees and multiply that fraction by the total area of the circle using the formula \frac{\theta}{360^\circ} \times \pi r^2.
What is the difference between a minor sector and a major sector?
A minor sector has a central angle less than 180 degrees, while a major sector has a central angle greater than 180 degrees.

Keep Learning

Area of a SectorLength of an ArcSegment of a Circle