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17
0
๐ฟ๐ฝ๐ฟ
14/07/2025
Maths
Finding the Circumference and Area of a Circle Revision Note
677
โข
14 Jul 2025
โข
Easy Circle Tricks: How to Find Circumference, Diameter, and Radius
Visual Representation of Circle Components
This page provides visual representations of the key components of a circle:
The radius is clearly illustrated as a line segment extending from the center of the circle to its edge. This visual aid helps students understand that the radius is always half the length of the diameter.
The diameter is depicted as a line segment that spans the entire width of the circle, passing through its center. This illustration emphasizes that the diameter is twice the length of the radius.
Highlight: The diameter is always twice the length of the radius in any circle.
These visual representations are crucial for students to grasp the spatial relationships between different parts of a circle, which is fundamental for solving more complex geometric problems involving circles.
Calculating Circumference: Example 1
This page demonstrates how to find the circumference of a circle using a given diameter:
The problem presents a circle with a diameter of 25 cm. To calculate the circumference, we use the formula:
Circumference = ฯ ร diameter
Example: Using ฯ โ 3.14 and diameter = 25 cm: Circumference = 3.14 ร 25 = 78.5 cm
Highlight: The answer may need to be expressed in cmยฒ, resulting in 78.5 cmยฒ.
This example illustrates the straightforward application of the circumference formula when the diameter is known. It also reminds students to pay attention to units in their final answer.
Calculating Circumference: Example 2
This page provides another example of how to calculate the circumference of a circle, reinforcing the concept:
The problem presents a circle with a diameter of 34 cm. Using the same formula as before:
Circumference = ฯ ร diameter
Example: With ฯ โ 3.14 and diameter = 34 cm: Circumference = 3.14 ร 34 = 106.76 cm
Highlight: The answer is rounded to one decimal place: 106.8 cm
This example not only reinforces the application of the circumference formula but also introduces the concept of rounding in mathematical calculations, an important skill in practical problem-solving.
Finding Diameter from Circumference: Example 1
This page demonstrates how to find the diameter of a circle when given its circumference:
The problem presents a circle with a circumference of 35 cm. To find the diameter, we rearrange the circumference formula:
Diameter = Circumference รท ฯ
Example: With circumference = 35 cm and ฯ โ 3.14: Diameter = 35 รท 3.14 = 11.15 cm
Highlight: The answer may need to be expressed to one decimal place in cmยฒ, resulting in 11.1 cmยฒ.
This example illustrates how to manipulate the circumference formula to solve for diameter, an important skill in geometric problem-solving.
Finding Diameter from Circumference: Example 2
This page provides another example of how to calculate the diameter of a circle from its circumference:
The problem presents a circle with a circumference of 20 cm. Using the rearranged formula:
Diameter = Circumference รท ฯ
Example: With circumference = 20 cm and ฯ โ 3.14: Diameter = 20 รท 3.14 = 6.37 cm
Highlight: The final answer is 6.4 cmยฒ
This example reinforces the process of finding the diameter from the circumference and emphasizes the importance of rounding and using correct units in the final answer.
Calculating Area Using Radius: Example 1
This page demonstrates how to find the area of a circle using its radius:
The problem presents a circle with a radius of 15 cm. To calculate the area, we use the formula:
Area = ฯ ร radiusยฒ
Example: With ฯ โ 3.14 and radius = 15 cm: Area = 3.14 ร 15ยฒ = 3.14 ร 225 = 706.5 cmยฒ
Highlight: The final answer is 706.5 cmยฒ
This example introduces the formula for calculating the area of a circle and demonstrates how to square the radius in the calculation.
Calculating Area Using Radius: Example 2
This page provides another example of how to calculate the area of a circle using its radius:
The problem presents a circle with a radius of 7 cm. Using the same formula as before:
Area = ฯ ร radiusยฒ
Example: With ฯ โ 3.14 and radius = 7 cm: Area = 3.14 ร 7ยฒ = 3.14 ร 49 = 153.9 cmยฒ
Highlight: The final answer is 153.9 cmยฒ
This example reinforces the application of the area formula for circles and provides additional practice in squaring the radius and performing the calculation.
Understanding Circle Basics
This page introduces the fundamental concepts related to circles:
Circumference is defined as the perimeter or distance around a circle. It's a crucial measurement in many geometric calculations.
Radius is described as the line segment that extends from the edge of a circle to its midpoint or center. It's half the length of the diameter.
Diameter is explained as the line segment that passes through the center of the circle, connecting two points on the circumference. It's twice the length of the radius.
Vocabulary: Circumference - The distance around a circle Vocabulary: Radius - The distance from the center to the edge of a circle Vocabulary: Diameter - The distance across a circle through its center
The page also includes simple diagrams illustrating these concepts, helping students visualize the relationships between these elements of a circle.
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The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
Best app on earth! no words because itโs too good
Thomas R
iOS user
Just amazing. Let's me revise 10x better, this app is a quick 10/10. I highly recommend it to anyone. I can watch and search for notes. I can save them in the subject folder. I can revise it any time when I come back. If you haven't tried this app, you're really missing out.
Basil
Android user
This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.
Rohan U
Android user
I know a lot of apps use fake accounts to boost their reviews but this app deserves it all. Originally I was getting 4 in my English exams and this time I got a grade 7. I didnโt even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as Iโm sure you too will see developments.
Xander S
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH ๐๐๐ฒ๐ค๐โจ๐๐ฎ
Elisha
iOS user
This apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now
Paul T
iOS user
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
Best app on earth! no words because itโs too good
Thomas R
iOS user
Just amazing. Let's me revise 10x better, this app is a quick 10/10. I highly recommend it to anyone. I can watch and search for notes. I can save them in the subject folder. I can revise it any time when I come back. If you haven't tried this app, you're really missing out.
Basil
Android user
This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.
Rohan U
Android user
I know a lot of apps use fake accounts to boost their reviews but this app deserves it all. Originally I was getting 4 in my English exams and this time I got a grade 7. I didnโt even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as Iโm sure you too will see developments.
Xander S
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH ๐๐๐ฒ๐ค๐โจ๐๐ฎ
Elisha
iOS user
This apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now
Paul T
iOS user
Easy Circle Tricks: How to Find Circumference, Diameter, and Radius
This guide explains key concepts and calculations related to circles, focusing on how to find the circumference of a circle, how to find the area of a circle, and how to find the radius of a circle.... Show more
Visual Representation of Circle Components
This page provides visual representations of the key components of a circle:
The radius is clearly illustrated as a line segment extending from the center of the circle to its edge. This visual aid helps students understand that the radius is always half the length of the diameter.
The diameter is depicted as a line segment that spans the entire width of the circle, passing through its center. This illustration emphasizes that the diameter is twice the length of the radius.
Highlight: The diameter is always twice the length of the radius in any circle.
These visual representations are crucial for students to grasp the spatial relationships between different parts of a circle, which is fundamental for solving more complex geometric problems involving circles.
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
Calculating Circumference: Example 1
This page demonstrates how to find the circumference of a circle using a given diameter:
The problem presents a circle with a diameter of 25 cm. To calculate the circumference, we use the formula:
Circumference = ฯ ร diameter
Example: Using ฯ โ 3.14 and diameter = 25 cm: Circumference = 3.14 ร 25 = 78.5 cm
Highlight: The answer may need to be expressed in cmยฒ, resulting in 78.5 cmยฒ.
This example illustrates the straightforward application of the circumference formula when the diameter is known. It also reminds students to pay attention to units in their final answer.
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
Calculating Circumference: Example 2
This page provides another example of how to calculate the circumference of a circle, reinforcing the concept:
The problem presents a circle with a diameter of 34 cm. Using the same formula as before:
Circumference = ฯ ร diameter
Example: With ฯ โ 3.14 and diameter = 34 cm: Circumference = 3.14 ร 34 = 106.76 cm
Highlight: The answer is rounded to one decimal place: 106.8 cm
This example not only reinforces the application of the circumference formula but also introduces the concept of rounding in mathematical calculations, an important skill in practical problem-solving.
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Finding Diameter from Circumference: Example 1
This page demonstrates how to find the diameter of a circle when given its circumference:
The problem presents a circle with a circumference of 35 cm. To find the diameter, we rearrange the circumference formula:
Diameter = Circumference รท ฯ
Example: With circumference = 35 cm and ฯ โ 3.14: Diameter = 35 รท 3.14 = 11.15 cm
Highlight: The answer may need to be expressed to one decimal place in cmยฒ, resulting in 11.1 cmยฒ.
This example illustrates how to manipulate the circumference formula to solve for diameter, an important skill in geometric problem-solving.
Sign up to see the contentIt's free!
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Improve your grades
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By signing up you accept Terms of Service and Privacy Policy
Finding Diameter from Circumference: Example 2
This page provides another example of how to calculate the diameter of a circle from its circumference:
The problem presents a circle with a circumference of 20 cm. Using the rearranged formula:
Diameter = Circumference รท ฯ
Example: With circumference = 20 cm and ฯ โ 3.14: Diameter = 20 รท 3.14 = 6.37 cm
Highlight: The final answer is 6.4 cmยฒ
This example reinforces the process of finding the diameter from the circumference and emphasizes the importance of rounding and using correct units in the final answer.
Sign up to see the contentIt's free!
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Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
Calculating Area Using Radius: Example 1
This page demonstrates how to find the area of a circle using its radius:
The problem presents a circle with a radius of 15 cm. To calculate the area, we use the formula:
Area = ฯ ร radiusยฒ
Example: With ฯ โ 3.14 and radius = 15 cm: Area = 3.14 ร 15ยฒ = 3.14 ร 225 = 706.5 cmยฒ
Highlight: The final answer is 706.5 cmยฒ
This example introduces the formula for calculating the area of a circle and demonstrates how to square the radius in the calculation.
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Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
Calculating Area Using Radius: Example 2
This page provides another example of how to calculate the area of a circle using its radius:
The problem presents a circle with a radius of 7 cm. Using the same formula as before:
Area = ฯ ร radiusยฒ
Example: With ฯ โ 3.14 and radius = 7 cm: Area = 3.14 ร 7ยฒ = 3.14 ร 49 = 153.9 cmยฒ
Highlight: The final answer is 153.9 cmยฒ
This example reinforces the application of the area formula for circles and provides additional practice in squaring the radius and performing the calculation.
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
Understanding Circle Basics
This page introduces the fundamental concepts related to circles:
Circumference is defined as the perimeter or distance around a circle. It's a crucial measurement in many geometric calculations.
Radius is described as the line segment that extends from the edge of a circle to its midpoint or center. It's half the length of the diameter.
Diameter is explained as the line segment that passes through the center of the circle, connecting two points on the circumference. It's twice the length of the radius.
Vocabulary: Circumference - The distance around a circle Vocabulary: Radius - The distance from the center to the edge of a circle Vocabulary: Diameter - The distance across a circle through its center
The page also includes simple diagrams illustrating these concepts, helping students visualize the relationships between these elements of a circle.
We thought youโd never ask...
What is the Knowunity AI companion?
Our AI Companion is a student-focused AI tool that offers more than just answers. Built on millions of Knowunity resources, it provides relevant information, personalised study plans, quizzes, and content directly in the chat, adapting to your individual learning journey.
Where can I download the Knowunity app?
You can download the app from Google Play Store and Apple App Store.
Is Knowunity really free of charge?
That's right! Enjoy free access to study content, connect with fellow students, and get instant help โ all at your fingertips.
Can't find what you're looking for? Explore other subjects.
Students love us โ and so will you.
4.9/5
App Store
4.8/5
Google Play
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
Best app on earth! no words because itโs too good
Thomas R
iOS user
Just amazing. Let's me revise 10x better, this app is a quick 10/10. I highly recommend it to anyone. I can watch and search for notes. I can save them in the subject folder. I can revise it any time when I come back. If you haven't tried this app, you're really missing out.
Basil
Android user
This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.
Rohan U
Android user
I know a lot of apps use fake accounts to boost their reviews but this app deserves it all. Originally I was getting 4 in my English exams and this time I got a grade 7. I didnโt even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as Iโm sure you too will see developments.
Xander S
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH ๐๐๐ฒ๐ค๐โจ๐๐ฎ
Elisha
iOS user
This apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now
Paul T
iOS user
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
Best app on earth! no words because itโs too good
Thomas R
iOS user
Just amazing. Let's me revise 10x better, this app is a quick 10/10. I highly recommend it to anyone. I can watch and search for notes. I can save them in the subject folder. I can revise it any time when I come back. If you haven't tried this app, you're really missing out.
Basil
Android user
This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.
Rohan U
Android user
I know a lot of apps use fake accounts to boost their reviews but this app deserves it all. Originally I was getting 4 in my English exams and this time I got a grade 7. I didnโt even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as Iโm sure you too will see developments.
Xander S
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH ๐๐๐ฒ๐ค๐โจ๐๐ฎ
Elisha
iOS user
This apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now
Paul T
iOS user