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.