Learning Materials
Features
Discover
A sector of a circle is an area of a circle where two of the sides are radii. An example of the sector (in red) is shown below:
Millions of flashcards designed to help you ace your studies
Sign up for freeWhat is Vaia?
How does Vaia help me study more efficiently?
Where can I find more explanations like this?
What's smart about Vaia's flashcards?
Can I create my own content on Vaia?
How does spaced repetition work in Vaia flashcards?
What can you do with flashcards in Vaia?
Is Vaia a science-based learning platform?
How do Vaia's smart learning plans support your exam prep?
Can you create your own study sets in Vaia?
What is Vaia?
How does Vaia help me study more efficiently?
Where can I find more explanations like this?
What's smart about Vaia's flashcards?
Can I create my own content on Vaia?
How does spaced repetition work in Vaia flashcards?
What can you do with flashcards in Vaia?
Is Vaia a science-based learning platform?
How do Vaia's smart learning plans support your exam prep?
Can you create your own study sets in Vaia?
Achieve better grades quicker with Premium
Geld-zurück-Garantie, wenn du durch die Prüfung fällst
Did you know that StudySmarter supports you beyond learning?
Review generated flashcards
Start learning or create your own AI flashcards
Team Sector of a Circle Teachers
A sector of a circle -Vaia Originals
An arc length is a part of the circle's circumference (perimeter). For the same sector, we could have arc as shown in green:
Arc length of a circle - Vaia Originals
You might already be familiar with this but let's look at calculating the area and arc length of a circle sector when the angle is given in degrees.
The formula to calculate the area of a sector with an angle \(\theta\) is:
\(\text{Area of a sector} = \pi \cdot r^2 \cdot \frac{\theta}{360}\)
where r is the radius of the circle
Circle A has a diameter of 10cm. A sector of circle A an angle of 50. What is the area of this sector?
\(\text{diameter = radius} \cdot 2\)
\(\text{radius} = \frac{\text{diameter}}{2} = \frac{10}{2} = 5 \space cm\)
The formula to calculate the arc length of a sector with an angle \(\theta\) is:
\(\text{Arc Length of a sector}: \pi \cdot d \cdot \frac{\theta}{360}\) where d is the diameter of the circle:
Circle B has a radius of 12cm. A sector within Circle B has an angle of 100. What is the length of the arc length of this sector?
You also need to be able to calculate the arc length and area of a sector of a circle where the angle is given in radians.
Radians are an alternative unit to degrees that we can use to measure an angle at the centre of the circle.
To recap, some common degree to radian conversions.
| Degrees | Radians |
| \(\frac{\pi}{6}\) | |
\(\frac{\pi}{4}\) | |
\(\frac{\pi}{3}\) | |
\(\frac{\pi}{2}\) | |
| \(\pi\) | |
\(\frac{3\pi}{2}\) | |
| \(2 \pi\) |
To calculate the area of a sector of a circle with an angle \(\theta^r\), the formula you use is:
\(\text{Area of a sector} = \frac{1}{2} \cdot r^2 \cdot \theta\)
where r is the radius of the circle.
Circle C has a radius of 15cm. Within Circle C, there is a sector with an angle of 0.5 radians. What is the area of this sector?
To calculate the arc length of a sector of a circle with an angle \(\theta^r\), the formula you use is:
\(\text{Arc length of a sector} = r \cdot \theta\), where r is the radius of the circle.
A sector in Circle D has an angle of 1.2 radians. Circle D has a diameter of 19. What is the arc length of this sector?
\(\text{Diameter = Radius} \cdot 2\text{ Radius} = \frac{\text{Diameter}}{2} = \frac{19}{2} = 9.5\)
\(\text{Arc Length of a sector} = \pi \cdot d \cdot \frac{\theta}{360}\)
Sign up for free to gain access to all our flashcards.
What is a sector of the circle?
A sector of a circle is a proportion of a circle where two sides are radii.
How do you find the sector of a circle?
To find the sector of a circle you need to use one of the formulas for the area of the sector. Which one you use is dependent on whether the angle at the centre is in radians or in degrees.
What are the formulas of the sector of the circle?
There are two formulas of a sector. One is to calculate the area of a sector of a circle. Area of a sector= pi × r^2 × (θ /360). The other one is to find the arc length of the sector of the circle. Arc length = pi × d × (θ /360)
At StudySmarter, we have created a learning platform that serves millions of students. Meet the people who work hard to deliver fact based content as well as making sure it is verified.
Lily Hulatt is a Digital Content Specialist with over three years of experience in content strategy and curriculum design. She gained her PhD in English Literature from Durham University in 2022, taught in Durham University’s English Studies Department, and has contributed to a number of publications. Lily specialises in English Literature, English Language, History, and Philosophy.
Get to know Lily
Gabriel Freitas is an AI Engineer with a solid experience in software development, machine learning algorithms, and generative AI, including large language models’ (LLMs) applications. Graduated in Electrical Engineering at the University of São Paulo, he is currently pursuing an MSc in Computer Engineering at the University of Campinas, specializing in machine learning topics. Gabriel has a strong background in software engineering and has worked on projects involving computer vision, embedded AI, and LLM applications.
Get to know Gabriel
Vaia is a globally recognized educational technology company, offering a holistic learning platform designed for students of all ages and educational levels. Our platform provides learning support for a wide range of subjects, including STEM, Social Sciences, and Languages and also helps students to successfully master various tests and exams worldwide, such as GCSE, A Level, SAT, ACT, Abitur, and more. We offer an extensive library of learning materials, including interactive flashcards, comprehensive textbook solutions, and detailed explanations. The cutting-edge technology and tools we provide help students create their own learning materials. StudySmarter’s content is not only expert-verified but also regularly updated to ensure accuracy and relevance.
Learn moreSave explanations to your personalised space and access them anytime, anywhere!
Sign up with Email Sign up with AppleBy signing up, you agree to the Terms and Conditions and the Privacy Policy of Vaia.
Already have an account? Log in
Sign up to highlight and take notes. It’s 100% free.
Explanations 
Textbooks 
Exams 
GCSE 
IGCSE 
AS 
A Level 
International A Level 
University Admissions Tests 
Flashcards 
Vaia AI 
Notes 
Study Plans 
Study Sets 
Find a job 
Find a degree 
Student Deals 
Magazine 
Mobile App 
