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.
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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 12 July 'Starter of the Day' page by Miss J Key, Farlingaye High School, Suffolk: "Thanks very much for this one. We developed it into a whole lesson and I borrowed some hats from the drama department to add to the fun!" Comment recorded on the 19 October 'Starter of the Day' page by E Pollard, Huddersfield: "I used this with my bottom set in year 9. To engage them I used their name and favorite football team (or pop group) instead of the school name. For homework, I asked each student to find a definition for the key words they had been given (once they had fun trying to guess the answer) and they presented their findings to the rest of the class the following day. They felt really special because the key words came from their own personal information." 
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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.
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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.
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Wednesday, January 9, 2019