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Construction NumeracyIntroduction to Circles Stonemasonry Department 2011
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Parts of a Circle Diameter Sector A straight line segment A portion of a circle Diameter which passes through which is defined by two the centre of the circle radii and an arc and the endpoints touch the perimeter of Sector the circle. Radius Tangent A straight line segment A straight line which Radius which joins the centre “just” touches the of the circle to any point outer perimeter of the on the perimeter of the Tangent circle circle Chord Circumference A straight line segment The length of the which does not pass Circumference perimeter of the circle through the centre of the circle and whose endpoints touch the perimeter of the circle.
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Pi (π) The symbol π (pronounced pie) is used to donate the mathematical constant which is the ratio of any circles circumference and area to its diameter. It is thought to consist of an infinite sequence of numbers but is generally shortened to 3.142
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Surface Area of a Circle Area = π r² Area = 3.142 x (5)² 5m Area = 3.142 x 25 Area = 78.55m² To calculate the area of a circle we square the radius of the circle then multiply the answer by pi (π). It is essential that you understand the difference between the radius and the diameter. Area = πr²
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Surface Area of a Circle Area = πr² 6m Area = 3.142 x (6)² Area = 113.11m² Area = πr² 8m Area = 3.142 x (8)² Area = 201.09m²
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Surface Area of a Circle Area = πr² 9m Area = 3.142 x (9)² Area = 254.50m² Area = πr² 6.4m Area = 3.142 x (6.4)² Area = 128.70m²
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Activity 1: Surface Areas Calculate the surface area of each of the circles shown below 6.8m 9.4m 145.29m² 277.63m² 5.25m 3.82m 86.60m² 45.85m²
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Activity 2: Surface Areas Calculate the surface area of each of the circles shown below 8.8m 12m 60.83m² 113.11m² 9.76m 4.32m 74.83m² 14.66m²
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Circumference of a Circle Circumference = π D 5m C = 3.142 x 10 C = 31.42m To calculate the circumference of a circle we multiply the diameter by pi (π). It is essential that you understand the difference between the radius and the diameter which is why in the example shown above the radius is 5m and the diameter is 10m. Circumference = π x Diameter
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Circumference of a Circle C=πxD 9m C = 3.142 x 9 C = 28.28m C=πxD 18m C = 3.142 x 18 C = 56.56m
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Circumference of a Circle C=πxD 6m C = 3.142 x 12 C = 37.70m C=πxD 8m C = 3.142 x 16 C = 50.27m
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Activity 3: Circumference Calculate the circumference of each of the circles shown below 8.8m 12m 27.65m 37.70m 9.76m 4.32m 30.67m 13.57m
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Activity 4: Circumference Calculate the circumference of each of the circles shown below 6.8m 9.4m 42.73m 59.06m 5.25m 3.82m 32.99m 24m
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Image References The image on the title slide of this presentation was sourced from Felix42 Contra La Censura’s photostream at: http://www.flickr.com/photos/felix42/413972905/ This image was made available under creative commons
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Developed by The Stonemasonry Department City of Glasgow College 2011
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