1. Construction Numeracy
Introduction to Circles
Stonemasonry Department 2011

2. 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.

3. 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

4. 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

5. 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

6. 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

7. 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

8. 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

9. 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

10. 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

11. 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

12. 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

13. 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

14. 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

15. Developed by The Stonemasonry Department
City of Glasgow College
2011