The Circle Introduction to circles Let’s investigate… Circumference Circumference examples

Starter Questions 7cm

Main part of a Circle Main parts of the circle radius Diameter Circumference

How can we measure the circumference? Let’s investigate… circumference We can use a ruler to measure the diameter. How can we measure the circumference?

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. 3.141592653589793238462643383279502… We’ll stop here since it would stretch for 600 miles if we printed them all!

Let’s Investigate... Circular Item Circumference Diameter Π

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. 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 C = d

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.

Example 1 6cm C = d C = x 6 C = 18.8cm (1 d.p.) 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.) 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

There is a much more accurate way! Area of a circle 1 ? 2 3 4 5 6 7 Mathematical Genius! 8 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 A = r² Remember: r² means r x r

Example 1 A = r² A = x 4 x 4 4m A = 50.3m² (1 d.p.) 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.) 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? Area of semi-circle = ½ x 452.4 =226.2m² First work out area of full circle. A semicircle is half a circle.