Calculations with Circles

1. Construction Numeracy Introduction to Circles Stonemasonry Department 2011

2. Parts of a Circle Diameter Radius Chord Sector Tangent Circumference Diameter A straight line segment which passes through the centre of the circle and the endpoints touch the perimeter of the circle. Radius A straight line segment which joins the centre of the circle to any point on the perimeter of the circle Chord A straight line segment which does not pass through the centre of the circle and whose endpoints touch the perimeter of the circle. Sector A portion of a circle which is defined by two radii and an arc Tangent A straight line which “just” touches the outer perimeter of the circle Circumference The length of the perimeter of the circle

3. Pi ( π ) 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 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 = π r² 5m

5. Surface Area of a Circle Area = π r² Area = 3.142 x (6)² Area = 113.11m² Area = π r² Area = 3.142 x (8)² Area = 201.09m² 6m 8m

6. Surface Area of a Circle Area = π r² Area = 3.142 x (9)² Area = 254.50m² 9m 6.4m Area = π r² Area = 3.142 x (6.4)² Area = 128.70m²

7. 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

8. 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

9. 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

10. 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

11. 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

12. 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

13. 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

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