Introduction to circles Area examples Let’s investigate… Circumference Circumference examples Area of a circle The Circle
www.mathsrevision.com Main part of a Circle Learning Intention To identify the main parts of a circle. Success Criteria 1.Know the terms circumference, diameter and radius. 2.Identify them on a circle. 3.Calculate the circumference using formula.
www.mathsrevision.com Main parts of the circle Main part of a Circle radius O Circumference Diameter
Let’s investigate… We can use a ruler to measure the diameter. How can we measure the circumference?
Let’s investigate… Work as a team at your table 1. Cut a piece of yarn that is exactly the length of the distance around the circular object at your table. (Called the circumference) 2. Cut another piece of yarn that is exactly the length of the distance through the middle of your circular object. (Called the diameter) 3. Use a ruler (in cm) to measure these two pieces of string. Be as accurate as possible! 4. Use a calculator to divide the Circumference by the diameter.
Let’s investigate… Look at the column circumference ÷ diameter circumference ÷ diameter is roughly 3.14
3.141592653589793238462643383279502… Let’s investigate… circumference ÷ diameter is roughly There isn’t an exact answer for this. It actually goes on forever! We’ll stop here since it would stretch for 600 miles if we printed them all! In 1989 a computer worked it out to 480 million decimal places. 3.14
The Circumference If it goes on for ever how can I write it down? We use the Greek letter instead. Mathematical Genius! This is called pi.
3.1415926535 So circumference ÷ diameter = Circumference = x diameter By re-arranging this we get: C = d The Circumference
This button stores to 8 or 9 decimal places which is more than accurate enough! 3.141592654 When doing circle calculations, you will normally use a calculator. Some calculators have a button like this: If your calculator doesn’t have Then use 3.14 instead. The Circumference
Example 1 6cm What is the circumference of this circle? C = dC = x 6 Press Then x 6 = C = 18.8cm
Example 2 5cm What is the circumference of this circle? C = dC = x 10 Remember: diameter = 2 x radius C = 31.4cm d =2 x 5= 10cm 10cm
Area of a circle To find the area we could try counting the squares inside the circle… 1 234 567 8 ? ? ? ? ?? ? ? There is a much more accurate way! Mathematical Genius!
Area of a circle A = r² Area = x radius There is a special formula for the area of a circle. Remember: r² means r x r
Example 1 What is the area of this circle? A = r²A = x 4 x 4 Press Then x 4 x4 = A = 50.3m² 4m
Example 2 What is the area of this circle? A = r²A = x 7 x 7 Press Then x 7 x 7 = A = 153.9cm² 14cm ? 7cm r =½ x 14= 7cm Don’t forget!
24m Example 3 What is the area of this semi-circle? A = r²A = x 12 x 12 A semicircle is half a circle. A = 452.4m² ? 12m r =½ x 24= 12m Don’t forget! Area of semi-circle = ½ x 452.4 First work out area of full circle. =226.2m²
Joke of the Day! What do you get when you take the circumference of an apple and divide it by the diameter of the apple? Apple Pi!