Please enter the code we just sent to whatsapp 91-11-46710500 to proceed
Didn't Receive OTP?
Geometry is an important part of mathematics. It helps us in solving problems related to shapes and sizes. It is an impactful tool which helps us to solve real life applications in fields like construction, art and science. There are various parts of geometry to be discussed about and today we are going to discuss the Sector of a circle.
A part of a circle that looks like a slice of a pizza. It is the area made up of two radii and an arc. There are three components of a sector. They are radius, arc and angle.
Radius is the line starting from the centre to the boundary of the circle.
The two sectors of a circle are -
1- Minor sector - the angle is less than 180 degrees
2- Major sector - the angle is greater than 180 degrees
Formulas-
Area of a Sector:
If the angle is in degrees:
Area = 360θ×πr2
If the angle is in radians:
Area = 21r2θ
Perimeter of sector
If the central angle θ is in degrees:
Perimeter = 2r+θ360×2πr
If the angle θ is in radians:
Perimeter = 2r+rθ
Arc Length of a Sector Formula
Length of the Arc:
If the angle is in degrees:
Arc Length = θ360×2πr
If the angle is in radians:
Arc Length = rθ
Q1: What is a sector in a circle?
A: A sector is a part of a circle enclosed between two radii and the arc between them.
Q2: What are the two types of sectors?
A: Minor Sector – angle < 180°
Major Sector – angle > 180°
Q3: Can a semicircle be called a sector?
A: Yes, a semicircle is a special case of a sector where the angle is exactly 180°.
Q4: Where do we see sectors in real life?
A: Pizza slices, Pie charts, Fan blades, Steering wheel movements, pie chart segment
Q5: Name the formula for the area of a circle?
A: The formula is - (θ/360°) × πr²
Example 1: Area (Radians)
Q: Radius = 5 m, angle = π3\frac{\pi}{3}3π radians. Find the area of the sector.
Formula:
Area = 21r2θ
Example 2: Real-Life Application
Q: A pizza has a radius of 10 inches. One slice makes a central angle of 45°.
a) Find the area of the slice.
b) Find the arc length (crust edge).
c) What is the total perimeter of that slice?
Sector of a circle is easy to solve once you follow the formulas. The kids should practice the sums with formulas regularly to master the problems. This concept is not only used in schools and colleges but also in different fields of construction, arts and science.
Alpha Math offers a game-based learning experience with a unique four-step approach to mastering every concept in math. Schedule a Free Class Now
Madhur Churiwala is an accomplished English and communicative skills educator with 15 years of experience. She holds a degree of B. ED in English. She started her career as a Fashion Designer but her passion for teaching and interacting with children turned her into a highly skilled educator. Initially she taught in school and then moved onto online teaching platform where she showcased her skills in education. Her way of teaching in fun and playful environment always inspires children to develop a love for learning. Over the years she has developed her passion for writing. As an author, Madhur brings her dedicated educational background to her blogs offering the valuable insights for educators, parents and students alike.
Unbox English
Little Yogi- Gita for kids
Alpha Math
