Circles  Using π  Level 5Practise using pi to calculate various circle measurements. 
This is 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. 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.
InstructionsTry 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. 



Transum.orgThis 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. 
More Activities: 

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 3 October 'Starter of the Day' page by S Mirza, Park High School, Colne: "Very good starters, help pupils settle very well in maths classroom." Comment recorded on the 16 March 'Starter of the Day' page by Mrs A Milton, Ysgol Ardudwy: "I have used your starters for 3 years now and would not have a lesson without one! Fantastic way to engage the pupils at the start of a lesson." 


AnswersThere are answers to this exercise but they are available in this space to teachers, tutors and parents who have logged in to their Transum subscription on this computer. A Transum subscription unlocks the answers to the online exercises, quizzes and puzzles. It also provides the teacher with access to quality external links on each of the Transum Topic pages and the facility to add to the collection themselves. Subscribers can manage class lists, lesson plans and assessment data in the Class Admin application and have access to reports of the Transum Trophies earned by class members. If you would like to enjoy adfree access to the thousands of Transum resources, receive our monthly newsletter, unlock the printable worksheets and see our Maths Lesson Finishers then sign up for a subscription now: Subscribe 

Go MathsLearning 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. Maths MapAre 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. TeachersIf you found this activity useful don't forget to record it in your scheme of work or learning management system. The short URL, ready to be copied and pasted, is as follows: 

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. 
Close
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.
Close
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 = πr^{2} [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.
Fermat's Library, Twitter
Wednesday, January 9, 2019