calculations with circles
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Construction NumeracyIntroduction to Circles
Stonemasonry Department 2011
Parts of a Circle
Diameter
Radius
Chor
d
Sector
Tangent
Circumference
DiameterA straight line segment which passes through the centre of the circle and the endpoints touch the perimeter of the circle.RadiusA straight line segment which joins the centre of the circle to any point on the perimeter of the circle
ChordA straight line segment which does not pass through the centre of the circle and whose endpoints touch the perimeter of the circle.
SectorA portion of a circle which is defined by two radii and an arc
TangentA straight line which “just” touches the outer perimeter of the circle
CircumferenceThe length of the perimeter of the circle
Pi (π)
πThe 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
Surface Area of a Circle
Area = π r²
Area = 3.142 x (5)²
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
5m
Surface Area of a Circle
Area = πr²
Area = 3.142 x (6)²
Area = 113.11m²
Area = πr²
Area = 3.142 x (8)²
Area = 201.09m²
6m
8m
Surface Area of a Circle
Area = πr²
Area = 3.142 x (9)²
Area = 254.50m²
9m
6.4m
Area = πr²
Area = 3.142 x (6.4)²
Area = 128.70m²
Activity 1: Surface Areas
6.8m
5.25m
9.4m
3.82m
Calculate the surface area of each of the circles shown below
145.29m²
86.60m²
277.63m²
45.85m²
Activity 2: Surface Areas
8.8m
9.76m
12m
4.32m
Calculate the surface area of each of the circles shown below
60.83m²
74.83m²
113.11m²
14.66m²
Circumference of a Circle
Circumference = π D
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
5m
Circumference of a Circle
C = π x D
C = 3.142 x 9
C = 28.28m
C = π x D
C = 3.142 x 18
C = 56.56m
9m
18m
Circumference of a Circle
C = π x D
C = 3.142 x 12
C = 37.70m
C = π x D
C = 3.142 x 16
C = 50.27m
6m
8m
Activity 3: Circumference
8.8m
9.76m
12m
4.32m
Calculate the circumference of each of the circles shown below
27.65m
30.67m
37.70m
13.57m
Activity 4: Circumference
6.8m
5.25m
9.4m
3.82m
Calculate the circumference of each of the circles shown below
42.73m
32.99m
59.06m
24m
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
Developed by The Stonemasonry DepartmentCity of Glasgow College
2011