
This is level 1; find the circumference given the radius or diameter. Give your answers correct to three significant figures. You can earn a trophy if you get at least 7 correct. The diagrams are not drawn to scale.
Try your best to answer the questions above. Type your answers into the boxes provided leaving no spaces. As you work through the exercise regularly click the “check” button. If you have any wrong answers, do your best to do corrections but if there is anything you don’t understand, please ask your teacher for help. When you have got all of the questions correct you may want to print out this page and paste it into your exercise book. If you keep your work in an ePortfolio you could take a screen shot of your answers and paste that into your Maths file. 

This web site contains over a thousand free mathematical activities for teachers and pupils. Click here to go to the main page which links to all of the resources available. Please contact me if you have any suggestions or questions. 


Mathematicians are not the people who find Maths easy; they are the people who enjoy how mystifying, puzzling and hard it is. Are you a mathematician? Comment recorded on the 14 October ‘Starter of the Day’ page by Inger Kisby, Herts and Essex High School: “Just a quick note to say that we use a lot of your starters. It is lovely to have so many different ideas to start a lesson with. Thank you very much and keep up the good work.” Comment recorded on the 26 March ‘Starter of the Day’ page by Julie Reakes, The English College, Dubai: “It’s great to have a starter that’s timed and focuses the attention of everyone fully. I told them in advance I would do 10 then record their percentages.” 
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Learning and understanding Mathematics, at every level, requires learner engagement. Mathematics is not a spectator sport. Sometimes traditional teaching fails to actively involve students. One way to address the problem is through the use of interactive activities and this web site provides many of those. The Go Maths page is an alphabetical list of free activities designed for students in Secondary/High school. Are you looking for something specific? An exercise to supplement the topic you are studying at school at the moment perhaps. Navigate using our Maths Map to find exercises, puzzles and Maths lesson starters grouped by topic. 



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Fermat’s Library, Twitter Wednesday, January 9, 2019 Do you have any comments? It is always useful to receive feedback and helps make this free resource even more useful for those learning Mathematics anywhere in the world. Click here to enter your comments. 
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Level 1 – find the circumference given the radius or diameter.
Level 2 – find the radius or diameter given the circumference.
Level 3 – find the area of a circle given either the radius or diameter.
Level 4 – the areas of circles are given, find either the radius, diameter or circumference.
Level 5 – the radius and angle subtended at the centre of the circle are given, find the length of the arc or area of the sector of the circle.
Level 6 – this level has mixed questions about the circle. Most of these questions will require a multipart calculation once the situation described in the question has been understood.
Areas of composite shapes requires an ability to calculate the areas of other shapes such as rectangles, triangles and trapezia.
Exam Style questions are in the style of GCSE or IB/Alevel exam paper questions and worked solutions are available for Transum subscribers.
Use a calculator for this exercise. All of the calculations you will do involve the number π (pronounced pi) which is roughly equal to 3.141592. You should use the π button on your calculator to get this number into your calculation.
Let r be the radius, d the diameter, C the circumference and A the area of a circle.
C = πd [i.e., to find the circumference multiply the length of the diameter by pi]
A = πr2 [i.e., to find the area multiply the square of the radius by pi]
For arcs multiply the circumference by the angle subtended at the centre and divide by 360.
For sector area multiply the circle area by the angle subtended at the centre and divide by 360.
For help using a calculator with circle calculations see Calculator Workout.
For more on this topic see our Circles page.
Answers to this exercise are available lower down this page when you are logged in to your Transum account. If you don’t yet have a Transum subscription one can be very quickly set up if you are a teacher, tutor or parent.
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