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Minor Sector

A minor sector is the region of a circle enclosed by two radii and the corresponding minor arc. It represents a fraction of the total area of the circle where the central angle is less than 180 degrees.

Key Concepts

A minor sector is formed when a circle is divided into two unequal parts by two radii; the smaller region is the minor sector.
The angle subtended by the minor arc at the center of the circle is called the central angle, which is always strictly less than 180 degrees.
The area of a minor sector is proportional to its central angle relative to the complete 360-degree angle of the circle.

Formula & Equation

Area=θ360∘×πr2Area = \frac{\theta}{360^\circ} \times \pi r^2

\theta is the central angle in degrees (where \theta < 180^\circ), 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 minor sector with a minor segment.
Fact: A minor sector is bounded by two radii and an arc (shaped like a pizza slice), whereas a minor segment is bounded by a chord and an arc.

Real World Applications

A single slice of a round pizza cut into several pieces represents a minor sector of the whole pizza.
The area swept by the minute hand of a clock between 12:00 and 12:15 forms a minor sector.

Frequently Asked Questions

How do you find the area of a minor sector?
You find the area by dividing the central angle by 360 degrees and multiplying the result by the total area of the circle.
What is the difference between a minor sector and a major sector?
A minor sector has a central angle less than 180 degrees and covers less than half the circle, while a major sector has a central angle greater than 180 degrees and covers more than half.

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