T Madas Circumference Perimeter of circle How do

© T Madas

Circumference = Perimeter of circle How do we work out the circumference of a circle? © T Madas

Circumference = Perimeter of circle The circumference of a circle is always “ 3 and bit” times its diameter. This “ 3 and a bit” is a special number called π (pi) ≈ 3. 14 π (pi) was first accurately computed by Archimedes. © T Madas

Circumference = Perimeter of of circle Circumference = r π = 3. 14 [2 d. p. ] d C= C= πx d 2 x π π x diameter 2 x π x radius special number it has its own name xr © T Madas

© T Madas

3. 1415926535897932384626433832795028841971693993751058209 749445923078164062862089986280348253421170679821480865132 823066470938446095505822317253594081284811174502841027019 385211055596446229489549303819644288109756659334461284756 482337867831652712019091456485669234603486104543266482133 936072602491412737245870066063155881748815209209628292540 917153643678925903600113305305488204665213841469519415116 094330572703657595919530921861173819326117931051185480744 623799627495673518857527248912279381830119491298336733624 406566430860213949463952247371907021798609437027705392171 762931767523846748184676694051320005681271452635608277857 713427577896091736371787214684409012249534301465495853710 1000 d. p. 507922796892589235420199561121290219608640344181598136297 747713099605187072113499999983729780499510597317328160963 185950244594553469083026425223082533446850352619311881710 100031378387528865875332083814206171776691473035982534904 287554687311595628638823537875937519577818577805321712268 06613001927876611195909216420198… © T Madas

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4610867639958916145855058397274209809097817293239301067663868240401113040247007350857828724627134946368531815469690466968693925472519413992914652423857762550047485295476814795467007050347999588867695016124972282040303995463 27883069597624936151010243655535223069061294938859901573466102371223547891129254769617928060721268039226911027772261025441492215765045081206771735712027180242968106203776578837166909109418074487814049075517… 20 000 d. p. © T Madas

Examples © T Madas

[1 d. p. ] C = 2 x π x r C = 2 x π x 4 c c C = 37. 7 cm c c C = 2 x π x r C = 2 x π x 6 A circle has a radius of 4 m. Find its circumference. 4 m 6 cm A circle has a radius of 6 cm. Find its circumference. C = 25. 1 m [1 d. p. ] © T Madas

A circle has a diameter of 1 m. Find its circumference. C = 6. 3 cm [1 d. p. ] C= C= πxd πx 1 c c πxd πx 2 c c C= C= 1 m 2 cm A circle has a diameter of 2 cm. Find its circumference. C = 3. 1 m [1 d. p. ] © T Madas

A circle has a circumference of 94 cm. Find its diameter. d = 94 ÷ π c c c d C=π xd d= C ÷π d = 29. 92 cm [2 d. p. ] What is the circle’s radius? 29. 92 ÷ 2 = 15. 0 cm [1 d. p. ] © T Madas

A circle has a circumference of 1. 71 m. Find its radius. d = 1. 71 ÷ π c c c r C=π xd d= C ÷π d = 0. 544 m [3 d. p. ] What is the circle’s radius? 0. 544 ÷ 2 = 0. 272 m [3 d. p. ] What is the circle’s radius in cm? 27. 2 cm © T Madas

Worded Problems © T Madas

© T Madas

68 m The radius of the London Eye is approximately 68 metres. What distance do you cover to the nearest metre on a ride that lasts exactly 3 full turns of the wheel? Each time you go round you cover: the circumference of a circle with a radius of 68 metres. c c C = 2 x π x r C = 2 x π x 68 C = 427. 3 m [1 d. p. ] In 3 full turns you cover: 427. 3 x 3 ≈ 1282 m © T Madas

© T Madas

The circumference of this circular garden: C= 2 xπ xr C= 2 x π x 3. 2 c c 3. 2 m A circular garden of radius 3. 2 metres, is to be fenced. Fencing costs £ 5. 47 a metre. How much would it cost to fence this garden? C = 20. 11 m [2 d. p. ] The total cost for the fencing: 20. 11 x 5. 47 ≈ £ 110 © T Madas

© T Madas

The circumference of a £ 2 coin is approximately 7 cm. Calculate the radius of a £ 2 coin in mm, correct to 2 d. p. d= 7÷ 7 cm c c c r C=π xd d= C ÷π π d = 2. 228 cm [3 d. p. ] What is the coin’s radius? 2. 228 ÷ 2 = 1. 114 cm [3 d. p. ] What is the coin’s radius in mm? 11. 14 mm © T Madas

© T Madas

A wire is bent to form an earring in the shape shown below. The diameter of the earring is 2 cm. If the wire in the earring is straightened out and used to make a single circular loop, what diameter would it have? We need to find the length of the wire 2 cm 1 cm πxd πx 2 c c 1 cm C= C= C = 6. 28 cm [2 d. p. ] © T Madas

A wire is bent to form an earring in the shape shown below. The diameter of the earring is 2 cm. If the wire in the earring is straightened out and used to make a single circular loop, what diameter would it have? We need to find the length of the wire 1 cm C = 6. 28 cm [2 d. p. ] C= C= πxd πx 1 c c 2 cm πxd πx 2 c c 1 cm C= C= C = 3. 14 cm [2 d. p. ] Altogether 6. 28 + 3. 14 = 12. 56 cm © T Madas

A wire is bent to form an earring in the shape shown below. The diameter of the earring is 2 cm. If the wire in the earring is straightened out and used to make a single circular loop, what diameter would it have? Altogether 6. 28 + 3. 14 = 12. 56 cm 1 cm 2 cm 1 cm Altogether 6. 28 + 3. 14 = 12. 56 cm © T Madas

A wire is bent to form an earring in the shape shown below. The diameter of the earring is 2 cm. If the wire in the earring is straightened out and used to make a single circular loop, what diameter would it have? Altogether 6. 28 + 3. 14 = 12. 56 cm 1 cm 2 cm 12. 56 ÷ π = 4 cm © T Madas

© T Madas

6 m In a funfair the radius of a Ferris wheel is 6 metres. What distance do you cover to the nearest metre on a ride that lasts exactly 7 full turns of the wheel? Each time you go round you cover: the circumference of a circle with a radius of 6 metres. c c C = 2 x π x r C = 2 x π x 6 C = 37. 7 m [1 d. p. ] £ 5 In 7 full turns you cover: 37. 7 x 7 ≈ 264 m © T Madas

© T Madas

150 cm King Arthur’s circular table is reputed to have had a radius of 5 feet. Every person sitting around this table, requires 60 cm of space. How many people can sit around this table? 60 cm [1 foot = 30 cm] The circumference: c c π xr C = 2 x π x 150 C= 2 x C = 942. 5 cm [1 d. p. ] How many 60 cm spaces can we get out of 942. 5 cm? 942. 5 ÷ 60 ≈ 15. 7 15 people © T Madas

© T Madas

A rectangle measuring 5 cm by 12 cm is drawn inside a circle, whose centre is at point O. Calculate the circumference of the circle, correct to 3 s. f. 52 + 122 = d 2 25 + 144 = d 2 5 cm d d 2 = 169 O d = 169 d = 13 cm 12 cm c C = π x 13 C = 40. 8 cm c C=πxd c c By Pythagoras Theorem: [3 s. f. ] © T Madas

© T Madas

A window consists of a rectangular frame and a semicircular part with 3 additional supports as shown below. 1. 1 m Calculate the total length of the material used for this window. 1. 2 m © T Madas

A window consists of a rectangular frame and a semicircular part with 3 additional supports as shown below. Calculate the total length of the material used for this window. 1. 1 + 1. 2 + 1. 1 + 1. 2 = 4. 6 0. 6 + 0. 6 = 1. 8 1. 1 m 0. 6 m π x 1. 2 ÷ 2 ≈ 1. 88 7. 28 1. 2 m The total length used for this window is 7. 28 metres (2 d. p. ) © T Madas

© T Madas

A tin has a radius of 3. 8 cm and a label is stuck all the way round the side of the tin. How long is the label, to the nearest cm? 3. 8 C = 24 cm c c C = 2 x π x r C = 2 x π x 3. 8 [nearest cm] © T Madas

© T Madas

A car is travelling at 90 km per hour. The radius of the wheels of the car is 25 cm. How many times does each wheel turn every second? We are going to work in metres and seconds 90 km in 1 hour x 1000 90000 m in 1 hour 25 cm 90 km/h = 25 m/s x 60 90000 m in 60 minutes x 60 90000 m in 3600 seconds ÷ 3600 25 m in 1 second © T Madas

A car is travelling at 90 km per hour. The radius of the wheels of the car is 25 cm. How many times does each wheel turn every second? We are going to work in metres and seconds C = 2 x π x 0. 25 c c C = 2πr 25 cm 90 km/h = 25 m/s C ≈ 1. 571 m 1 turn of the wheel is 1. 571 m Every second the wheel covers 25 m 25 ÷ 1. 571 ≈ 15. 9 turns When the car is travelling at 90 km/h, its wheels turn at the approximate rate of 16 turns every second. © T Madas

© T Madas