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

To identify the main parts of a circle. 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

Main part of a Circle Main parts of the circle radius Diameter Circumference www.mathsrevision.com

Starter Questions www.mathsrevision.com Q1. Calculate Q2. Convert 60% to fraction and simplify. Q3. Convert to a percentage. 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

Let’s investigate… circumference www.mathsrevision.com We can use a ruler to measure the diameter. How can we measure the circumference? www.mathsrevision.com Ask your teacher for the circles worksheet.

circumference ÷ diameter Let’s investigate… Look at the column circumference ÷ diameter 3 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!

If it goes on for ever how can I write it down? The Circumference If it goes on for ever how can I write it down? Mathematical Genius! We use the Greek letter instead. www.mathsrevision.com This is called pi.

The Circumference Circumference = x diameter C = d So circumference ÷ diameter = 3.1415926535 By re-arranging this we get: Circumference = x diameter www.mathsrevision.com C = d

Starter Questions www.mathsrevision.com 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

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! www.mathsrevision.com 3.141592654 If your calculator doesn’t have Then use 3.14 instead.

Example 1 6cm C = d C = x 6 C = 18.8cm (1 d.p.) www.mathsrevision.com Press Then x 6 = What is the circumference of this circle?

Example 2 C = d d = 2 x 5 = 10cm 10cm C = x 10 5cm C = 31.4cm (1 d.p.) www.mathsrevision.com What is the circumference of this circle? Remember: diameter = 2 x radius

Go back to the Circles worksheet and use The Circumference Go back to the Circles worksheet and use to work out the circumference of each circle. C = d www.mathsrevision.com

Starter Questions www.mathsrevision.com www.mathsrevision.com

There is a much more accurate way! Area of a circle 1 ? 2 3 4 5 6 7 Mathematical Genius! 8 www.mathsrevision.com To find the area we could try counting the squares inside the circle… There is a much more accurate way!

There is a special formula for the area of a circle. x radius www.mathsrevision.com A = r² Remember: r² means r x r

Example 1 A = r² A = x 4 x 4 4m A = 50.3m² (1 d.p.) www.mathsrevision.com Press Then x 4 x4 = What is the area of this circle?

Example 2 ? A = r² r = ½ x 14 = 7cm 7cm A = x 7 x 7 14cm Don’t forget! r = ½ x 14 = 7cm ? 7cm A = x 7 x 7 14cm A = 153.9cm² (1 d.p.) www.mathsrevision.com Press Then x 7 x 7 = What is the area of this circle?

Example 3 ? A = r² 24m r = ½ x 24 = 12m 12m A = x 12 x 12 Don’t forget! 24m r = ½ x 24 = 12m 12m ? A = x 12 x 12 A = 452.4m² (1 d.p.) What is the area of this semi-circle? www.mathsrevision.com Area of semi-circle = ½ x 452.4 =226.2m² First work out area of full circle. A semicircle is half a circle.