Homeclass 10MathsAreas Related to CirclesMajor Sector

Major Sector

A major sector is the larger region of a circle enclosed by two radii and the corresponding major arc. It represents the portion of the circle where the central angle is greater than 180 degrees, covering more than half of the total circular area.

Key Concepts

It is bounded by two radii and the major arc, which is the longer curved section of the circle's circumference.
The central angle subtended by a major sector is always a reflex angle, measuring between 180 degrees and 360 degrees.
The combined area of a major sector and its corresponding minor sector is exactly equal to the total area of the circle.

Formula & Equation

AreaofMajorSector=360∘−θ360∘×πr2Area of Major Sector = \frac{360^\circ - \theta}{360^\circ} \times \pi r^2

r represents the radius of the circle, \theta represents the central angle of the corresponding minor sector in degrees, and \pi is a mathematical constant approximately equal to 3.14159.

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Common Misconceptions

Myth: Students often confuse the major sector with the major arc.
Fact: The major arc is only the curved one-dimensional outer boundary line of the circle, whereas the major sector is the entire two-dimensional area enclosed by that arc and the two radii.

Real World Applications

A whole pizza with a single slice removed, where the remaining larger portion of the pizza represents the major sector.
A pie chart displaying demographic data where the dominant category occupies more than 50 percent of the circular graph.

Frequently Asked Questions

How do you calculate the area of a major sector?
You can calculate it by subtracting the area of the minor sector from the total area of the circle, or by using the reflex central angle in the sector area formula.
What is the central angle of a major sector?
The central angle of a major sector is always a reflex angle, meaning it is strictly greater than 180 degrees and less than 360 degrees.

Keep Learning

Sector of a CircleMinor SectorArea of a Sector