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
www.mathsrevision.com Main parts of the circle Main part of a Circle radius O Circumference Diameter
www.mathsrevision.com www.mathsrevision.com Starter Questions www.mathsrevision.com Q1.Calculate Q2.Convert 60% to fraction and simplify. Q3.Convert Q4.What is the time difference 09:28 and 10:50 to a percentage. Q5.The answer to the question is 90. What is the question.
Let’s investigate… We can use a ruler to measure the diameter. How can we measure the circumference? Ask your teacher for the circles worksheet. www.mathsrevision.com
3.141592653589793238462643383279502… Let’s investigate… Look at the column circumference ÷ diameter 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 www.mathsrevision.com
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 www.mathsrevision.com The Circumference
www.mathsrevision.com www.mathsrevision.com Starter Questions www.mathsrevision.com Q1.Tidy up the expression Q2.Calculate Q3.Round to 1 decimal place. Q4.12.5 % as a fraction (a)2.34(b)10.25(c)3.23
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. www.mathsrevision.com The Circumference
Example 1 6cm What is the circumference of this circle? C = dC = x 6 Press Then x 6 = C = 18.8cm (1 d.p.) www.mathsrevision.com
Example 2 5cm What is the circumference of this circle? C = dC = x 10 Remember: diameter = 2 x radius C = 31.4cm (1 d.p.) d =2 x 5= 10cm 10cm www.mathsrevision.com
Go back to the Circles worksheet and use to work out the circumference of each circle. C = d www.mathsrevision.com The Circumference
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!
www.mathsrevision.com 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 (1 d.p.) 4m www.mathsrevision.com
Example 2 What is the area of this circle? A = r²A = x 7 x 7 Press Then x 7 x 7 = A = 153.9cm² (1 d.p.) 14cm ? 7cm r =½ x 14= 7cm Don’t forget! www.mathsrevision.com
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 (1 d.p.) ? 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