The Circle Monday 4 June 20121. Know the names of a circle’s features2. Calculate the circumference3. Calculate an arc length4. Deal with the revolution of wheels and journey problem Why am Levels 5 8 I doingA wheel is a circle! this?Circles in design – Mickey OK -Mouse is made from circles WhatA real favourite SAT and have I gotGCSE question to do?
Name these Features The distance from the centre to the edge The distance from one side to the other passing through the centre The distance all of the way round the edge The blue line Area Circumference Rotation RadiusDegree Chord Sector Segment Diameter Sphere Concentric Arc
The distance from the centre to the edge RADIUS The distance from one side to theSegment other passing through the centre Sector DIAMETER The distance all of the way round the edge CIRCUMFERENCE An ARC is the name The blue line CHORD for part of the circumference Where can you see i) a segment ii) a sector iii) an arc?
APPROXIMATELY what is the relationship (connection)between a circle’s diameter and its circumference?
To APPROXIMATELY find theCIRCUMFERENCE MULTIPLY the DIAMETER by 3 (C = 3 x d) Radius Diameter Circumference 4 8 12 10 5 15 18 30 42
To APPROXIMATELY find theCIRCUMFERENCE MULTIPLY the DIAMETER by 3 (C = 3 x d) Radius Diameter Circumference 2 4 12 4 8 24 6 12 36 10 20 60 5 10 30 15 30 90 3 6 18 5 10 30 7 14 42
SAT Aural Question ( Answer a question in 10 seconds)• A circle has a diameter of 10 cm. APPROXIMATELY (ROUGHLY), what is its circumference? 30 cm• A circle has a circumference of 18 cm. Approximately, what is its diameter? 6 cm
Calculate the CircumferenceUsing the Correct Formula Level 6
How to calculate the circumferenceEvaluate the Always, writeCIRCUMFERENCE C= d the formula (rule) Diameter = 12 cm C = 3.14 X 12 C = 37.68 The symbol is the Greek letter pi. It stands for a number that can never be found exactly. It is approximately 3.14
How to calculate the diameter from the circumference Always, writeIf thecircumference is 40 C= d the formula (rule)cm. evaluate theDIAMETER d=C÷ Diameter = ?cm d = C ÷ 3.14 d = 40 ÷ 3.14 d = 12.73
How to Calculate an Arc Calculate the arc lengthLength A AB for a circle with a diameter of 12 cm. 720 Circumference B C = 3.14 x 12 C = 37.6 cmBut we only want the arc lengthAB. This is 720 of the circle and AB = 0.2 x Cbecause there are 3600 in a AB = 0.2 x 37.6circle, this is 72 ÷ 360 = 0.2 as AB = 5.52a decimal fraction of thecircumference
The FORMULA for an Calculate the arc lengthArc Length A AB for a circle with a diameter of d x 0 AB = x/360( d) B AB = (x ÷ 360) x 3.14 x d Divide the arc length’s angle by 360 then multiply this by the circumference
Using the FORMULA for Calculate the arc lengthan Arc A AB for these circles AB = x/360( d) x0 B AB = (x ÷ 360) x 3.14 x d X0 Diam Arc AB X0 Diam Arc AB 1. 144 12 4. 270 60 2. 48 40 5. 24 36 3. 180 25 6. 70 40
Using the FORMULA for Calculate the arc lengthan Arc A AB for these circles AB = x/360( d) x0 B AB = (x ÷ 360) x 3.14 x d X0 Diam Arc AB X0 Diam Arc AB 1. 144 12 15.07 4. 270 60 141.3 2. 48 40 20.10 5. 24 36 7.54 3. 180 25 39.25 6. 70 40 24.42
Finding the Number of Revolutions(turns) of a Wheel on a Journey Level 8
A wheel with a spotof blue paint The wheel turns once This distance is the circumference When a wheel makes one complete revolution, the distance that it travels is its circumference
How many times will a wheel with a diameter of 0.5metre rotate when it travels distance of 100 metres? 100 metres 1.57 1. Find the circumference of the When a wheel wheel makes one complete C = 3.14 x 0.5 revolution, the C = 1.57 distance that it travels is its 2. Divide this into 100 to circumference find the number of revolutions Revs = 100 ÷ 1.57 Revs = 63.7 times
1. Find the circumference of the wheel C = 3.14 x d 2. Divide this into the journey to find the number of revolutions Revs = Journey Distance ÷ CWheel’s Circumference Distance of Number ofDiameter Journey Revolutions0.3 metres 120 metres0.4 metres 200 metres0.7 metres 150 metres0.6 metres 1000 metres
A bike’s wheels have adiameter of 70 cm.How many times willthe wheel revolveduring a journey of 50km? A car’s wheels have a diameter of 45 cm. How many times will the wheel revolve during a journey of 100 Level 8 km?