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## Introduction to circles

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**The Circle**Introduction to circles Let’s investigate… Circumference Circumference examples www.mathsrevision.com Area of a circle Area examples**Starter Questions**7cm www.mathsrevision.com**Main part of a Circle**Learning Intention To identify the main parts of a circle. • Success Criteria • Know the terms circumference, diameter and radius. • Identify them on a circle. • Calculate the circumference using formula. www.mathsrevision.com www.mathsrevision.com**radius**Diameter Circumference Main part of a Circle Main parts of the circle O www.mathsrevision.com**Starter Questions**Q1. Calculate Q2. Convert 60% to fraction and simplify. to a percentage. Q3. Convert www.mathsrevision.com Q4. What is the time difference 09:28 and 10:50 Q5. The answer to the question is 90. What is the question. www.mathsrevision.com**circumference**Let’s investigate… We can use a ruler to measure the diameter. How can we measure thecircumference? www.mathsrevision.com Ask your teacher for the circles worksheet.**3**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! In 1989 a computer worked it out to 480 million decimal places. www.mathsrevision.com 3.141592653589793238462643383279502… We’ll stop here since it would stretch for 600 miles if we printed them all!**We use the Greek letter**instead. The Circumference If it goes on for ever how can I write it down? Mathematical Genius! www.mathsrevision.com This is called pi.**The Circumference**So circumference ÷ diameter = 3.1415926535 By re-arranging this we get: x diameter Circumference = www.mathsrevision.com d C =**Starter Questions**Q1. Tidy up the expression Q2. Calculate Q3. Round to 1 decimal place. www.mathsrevision.com (a) 2.34 (b) 10.25 (c) 3.23 Q4. 12.5 % as a fraction www.mathsrevision.com**When doing circle calculations, you will normally use a**calculator. This button stores to 8 or 9 decimal places which is more than accurate enough! If your calculator doesn’t have Then use 3.14 instead. The Circumference Some calculators have a button like this: www.mathsrevision.com 3.141592654**C = d**C = x 6 Press Then x 6 = Example 1 6cm C = 18.8cm (1 d.p.) www.mathsrevision.com What is the circumference of this circle?**C = d**C = x 10 Example 2 d = 2 x 5 = 10cm 10cm C = 31.4cm (1 d.p.) 5cm www.mathsrevision.com What is the circumference of this circle? Remember: diameter = 2 x radius**The Circumference**Go back to the Circles worksheet and use to work out the circumference of each circle. d C = www.mathsrevision.com**Starter Questions**www.mathsrevision.com www.mathsrevision.com**?**? ? ? ? ? 8 7 6 5 1 2 4 3 ? ? Area of a circle Mathematical Genius! www.mathsrevision.com To find the area we could try counting the squares inside the circle… There is a much more accurate way!**x radius**x radius Area = r² A = Area of a circle There is a special formula for the area of a circle. www.mathsrevision.com Remember: r² means r x r**A = r²**A = x 4 x 4 Press Then x 4 x4 = Example 1 4m A = 50.3m² (1 d.p.) www.mathsrevision.com What is the area of this circle?**A = r²**A = x 7 x 7 Press Then x 7 x 7 = Example 2 Don’t forget! r = ½ x 14 = 7cm ? 7cm A = 153.9cm² (1 d.p.) 14cm www.mathsrevision.com What is the area of this circle?**A = r²**A = x 12 x 12 24m Example 3 Don’t forget! r = ½ x 24 = 12m ? 12m A = 452.4m² (1 d.p.) What is the area of this semi-circle? Area of semi-circle www.mathsrevision.com = ½ x 452.4 =226.2m² A semicircle is half a circle. First work out area of full circle.