What is a Major Sector?

S3-SA2-0091

Grade Level:

Class 6

AI/ML, Data Science, Physics, Economics, Cryptography, Computer Science, Engineering

Definition

What is it?

A major sector is the larger part of a circle when it is divided into two sectors by two radii. Imagine cutting a pizza into two unequal slices; the bigger slice is the major sector. It always has an angle greater than 180 degrees at the center of the circle.

Simple Example

Quick Example

Think of a clock showing 3:00 PM. The hands divide the clock face into two parts. The smaller part (from 12 to 3) is the minor sector. The much larger part (from 3 all the way around to 12) is the major sector, covering most of the clock face.

Worked Example

Step-by-Step

PROBLEM: A circular garden has a sprinkler covering a 90-degree angle. What is the angle of the major sector of the garden not covered by the sprinkler?

Step 1: Understand the total angle in a circle. A full circle always has 360 degrees.
---Step 2: Identify the angle of the minor sector (the part covered by the sprinkler). This is given as 90 degrees.
---Step 3: To find the angle of the major sector, subtract the minor sector's angle from the total angle of the circle.
---Step 4: Calculation: Major Sector Angle = Total Circle Angle - Minor Sector Angle
---Step 5: Major Sector Angle = 360 degrees - 90 degrees
---Step 6: Major Sector Angle = 270 degrees.

ANSWER: The angle of the major sector not covered by the sprinkler is 270 degrees.

Why It Matters

Understanding major sectors helps in fields like Engineering to design curved structures, or in Data Science to visualize large portions of data in pie charts. Architects use this concept when planning curved buildings or large open spaces, and game developers use it for creating circular maps or effects.

Common Mistakes

MISTAKE: Confusing major sector with minor sector. | CORRECTION: The major sector is always the larger of the two parts, and its central angle is always greater than 180 degrees.

MISTAKE: Calculating the major sector angle by adding to 180 degrees. | CORRECTION: Always subtract the given minor sector angle from the total angle of a circle, which is 360 degrees.

MISTAKE: Thinking a major sector is only for circles divided exactly in half. | CORRECTION: A major sector exists whenever a circle is divided into two unequal sectors. If divided exactly in half, both parts are semicircles, not distinct major/minor sectors.

Practice Questions

Try It Yourself

QUESTION: If a circle has a minor sector with a central angle of 100 degrees, what is the angle of its major sector? | ANSWER: 260 degrees

QUESTION: A pizza is cut such that one slice (minor sector) has an angle of 75 degrees. If you eat the rest of the pizza, what is the angle of the part you ate (major sector)? | ANSWER: 285 degrees

QUESTION: A circular park has a walking track that covers a minor sector of 120 degrees. The remaining part of the park is covered with grass. If the total area of the park is 3600 sq meters, and the area is proportional to the central angle, what is the angle of the grassy area (major sector)? | ANSWER: 240 degrees

MCQ

Quick Quiz

Which of the following describes a major sector?

The smaller part of a circle formed by two radii.

A part of a circle with a central angle less than 180 degrees.

The larger part of a circle formed by two radii, with a central angle greater than 180 degrees.

Half of a circle.

The Correct Answer Is:

Option C correctly defines a major sector as the larger part of a circle with a central angle greater than 180 degrees. Options A and B describe a minor sector, and Option D describes a semicircle.

Real World Connection

In the Real World

When you look at a pie chart showing election results, if one party gets 70% of the votes, the segment representing their votes is a major sector because it's more than half. Data analysts use major sectors in these charts to easily show which category holds the largest share, for example, which brand of mobile phone is most popular in India.

Key Vocabulary

Key Terms

SECTOR: A part of a circle enclosed by two radii and an arc | RADIUS: A line segment from the center to any point on the circumference of a circle | CENTRAL ANGLE: The angle formed at the center of a circle by two radii | MINOR SECTOR: The smaller part of a circle formed by two radii and an arc, with an angle less than 180 degrees | CIRCLE: A round plane figure whose boundary consists of points equidistant from a fixed center point

What's Next

What to Learn Next

Now that you understand major sectors, you can learn about 'Area of a Sector'. This will teach you how to calculate the actual space covered by these parts of a circle, which is super useful in real-world problems!