www mathsrevision com The Circle Introduction to circles
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www. mathsrevision. com The Circle Introduction to circles Let’s investigate… Circumference examples Area of a circle Area examples
www. mathsrevision. com Starter Questions 7 cm
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 part of a Circle Main parts of the circle radius O Diameter Circumference www. mathsrevision. com
www. mathsrevision. com Starter Questions Q 1. Calculate Q 2. Convert 60% to fraction and simplify. Q 3. Convert Q 4. What is the time difference 09: 28 and 10: 50 Q 5. The answer to the question is 90. What is the question. to a percentage. www. mathsrevision. com
www. mathsrevision. com 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.
Let’s investigate… www. mathsrevision. com Look at the column circumference ÷ diameter is roughly 3 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. 3. 141592653589793238462643383279502… We’ll stop here since it would stretch for 600 miles if we printed them all!
www. mathsrevision. com The Circumference If it goes on for ever how can I write it down? Mathematical Genius! We use the Greek letter instead. This is called pi.
The Circumference www. mathsrevision. com So circumference ÷ diameter = 3. 1415926535 By re-arranging this we get: Circumference = C= x diameter d
www. mathsrevision. com Starter Questions Q 1. Tidy up the expression Q 2. Calculate Q 3. Round to 1 decimal place. (a) Q 4. 2. 34 (b) 10. 25 (c) 12. 5 % as a fraction www. mathsrevision. com 3. 23
www. mathsrevision. com The Circumference When doing circle calculations, you will normally use a calculator. Some calculators have a button like this: This button stores to 8 or 9 decimal places which is more than accurate enough! 3. 141592654 If your calculator doesn’t have Then use 3. 14 instead.
www. mathsrevision. com Example 1 6 cm What is the circumference of this circle? C= d C= x 6 C = 18. 8 cm (1 d. p. ) Press Then x 6=
www. mathsrevision. com Example 2 C= d d = 2 x 5 = 10 cm 5 cm What is the circumference of this circle? C= x 10 C = 31. 4 cm (1 d. p. ) Remember: diameter = 2 x radius
www. mathsrevision. com The Circumference Go back to the Circles worksheet and use C= d to work out the circumference of each circle.
www. mathsrevision. com Starter Questions www. mathsrevision. com
www. mathsrevision. com Area of a circle Mathematical Genius! ? 1 ? ? 2 3 4 ? ? 5 6 ? 8 7 ? ? To find the area we could try counting the squares inside the circle… There is a much more accurate way!
www. mathsrevision. com Area of a circle There is a special formula for the area of a circle. Area = x radius A= r² Remember: r² means r x r
www. mathsrevision. com Example 1 4 m What is the area of this circle? A= r² A= x 4 x 4 A = 50. 3 m² (1 d. p. ) Press Then x 4 =
www. mathsrevision. com Example 2 ? 7 cm 14 cm What is the area of this circle? A= r² r = ½ x 14 = 7 cm A= Don’t forget! x 7 x 7 A = 153. 9 cm² (1 d. p. ) Press Then x 7 =
www. mathsrevision. com Example 3 A= r² r = ½ x 24 = 12 m ? 24 m What is the area of this semi-circle? A= Don’t forget! x 12 A = 452. 4 m² (1 d. p. ) Area of semi-circle = ½ x 452. 4 =226. 2 m² First work out area of full circle. A semicircle is half a circle.
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