T Madas T Madas The circumference of this

The circumference of this circular garden: C= 2 xπ xr C= 2 x π

68 m The radius of the London Eye is approximately 68 metres. What distance

The circumference of a £ 2 coin is approximately 7 cm. Calculate the radius

6 m In a funfair the radius of a Ferris wheel is 6 metres.

150 cm King Arthur’s circular table is reputed to have had a radius of

A wire is bent to form an earring in the shape shown below. The

A rectangle measuring 5 cm by 12 cm is drawn inside a circle, whose

A window consists of a rectangular frame and a semicircular part with 3 additional

A tin has a radius of 3. 8 cm and a label is stuck

A car is travelling at 90 km per hour. The radius of the wheels

The area of this circular region: A = π x r 2 A= π

A circle and a semicircle, shown below have the same area. If the semicircle

The figure below shows two circles sharing the same centre O and having radii

The figure below shows a pond made up of two squares and two identical

Calculate the perimeter & area of the following shape: 4 m 16 m The

Calculate the perimeter & area of the following shape: 7 cm 28 cm C

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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

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

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

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

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

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

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

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

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

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

The area of this circular region: A = π x r 2 A= π x 4. 52 c c 4. 5 m In the local park a circular region of radius 4. 5 metres, is to have a new lawn laid. Turf costs £ 2. 20 a square metre. How much would it cost to turf this region? A = 63. 62 m 2 [2 d. p. ] The total cost for the turf: 63. 62 x 2. 2 ≈ £ 139. 95 © T Madas

A circle and a semicircle, shown below have the same area. If the semicircle has a radius of 8 cm, calculate the radius of the circle, correct to 3 significant figures. x 8 cm area of a circle A = πr 2 A = π x x 2 = πx 2 area of a circle A = πr 2 A = π x 82 area of the semicircle A = π x 8 2 x 1 = 32π 2 if x 2 = 32 , then x ≈ 5. 66 cm [3 s. f. ] © T Madas

The figure below shows two circles sharing the same centre O and having radii R and r with R > r. The shaded area is ¾ of the area of the larger circle. Express R in terms of r. πR 2 – π r 2 O πR 2 – R r Area of big circle: Area of small circle: Shaded Area: πR πr 2 πR 2 – π r 2 2 3 4 1 4 3 = 4 πR 2 ⇔ πR 2 = π r 2 ⇔ πR 2 = ⇔ 4πr 2 R 2 = 4 r 2 ⇔ R = 2 r © T Madas

The figure below shows two circles sharing the same centre O and having radii R and r with R > r. AB is a tangent to the smaller circle and has a length of 8 cm. 1. Write down an expression for the area of the shaded region. 2. Calculate the area of the shaded region, to 3 s. f. B O r R 4 A πR 2 πr 2 Shaded Area = πR 2 – π r 2 =π R 2 – r 2 = π x 16 Area of big circle = Area of small circle = ≈ 50. 3 cm 2 r 2 + 42 = R 2 ⇔ 16 = R 2 – r 2 © T Madas

The figure below shows a pond made up of two squares and two identical quarter circles with a radius of 4 m. Calculate to 2 decimal places: 1. the perimeter of the pond. 2. the area of the pond 4 m 4 m © T Madas

The figure below shows a pond made up of two squares and two identical quarter circles with a radius of 4 m. 4 6. 28 ? 4 m 4 4 4 m ? 6. 28 4 C = 2 xπxr C = 2 x π x 4 C ≈ 25. 13 m c c Calculate to 2 decimal places: 1. the perimeter of the pond. 2. the area of the pond Each curved edge is ¼ of the circumference of a full circle. 25. 13 ÷ 4 ≈ 6. 28 m P=4 x 4 + 2 x 6. 28 ≈ 28. 57 m © T Madas

The figure below shows a pond made up of two squares and two identical quarter circles with a radius of 4 m. 16 m 2 12. 57 m 2 4 m 16 m 2 4 m 12. 57 m 2 A A = = = ≈ πxr 2 π x 42 π x 16 c c c Calculate to 2 decimal places: 1. the perimeter of the pond. 2. the area of the pond 50. 27 m 2 2 m 50. 27 ÷ 4 12. 57 ≈ Area of a Quarter Circle P=2 x 16 + 2 x 12. 57 ≈ 57. 14 m 2 © T Madas

Calculate the perimeter & area of the following shape: 4 m 16 m The perimeter is equal to … … the circumference of … … 8 semi-circles of radius 4 m … … or … … 4 circles of radius 4 m … P = [2 x π x 4]x 4 P = 32 π P ≈ 100. 5 m C =2 x π xr A=π xr 2 © T Madas

Calculate the perimeter & area of the following shape: 4 m 16 m The total area is equal to … … the area of a square with side length of 16 m … … plus … … the area of 4 circles of radius 4 m … 2 A = 16 x 16 + [π x 4 ]x 4 C =2 x π xr A=π xr 2 A = 256 + 64 x π A ≈ 457 m 2 © T Madas

Calculate the perimeter & area of the following shape: 7 cm 28 cm C =2 x π xr A=π xr 2 The perimeter is equal to … … the circumference of a semi-circle of radius 14 cm … … plus … … the circumference of a circle of radius 7 cm … P = [2 x π x 14 ] x P = 14 π + 14 π P = 28 π 1 2 +2 x π x 7 P ≈ 88. 0 cm © T Madas

Calculate the perimeter & area of the following shape: 7 cm 28 cm C =2 x π xr A=π xr 2 The total area is equal to … … the area of a semi-circle of radius 14 cm … … less… … the area of a circle of radius 7 cm … A = [ π x 14 2 ] x A = 98 π – 49 π A = 49 π 1 2 – π x 72 A ≈ 154 cm 2 © T Madas