Find the Circumference of a Circle We are Learning to…… Find the Circumference of a Circle

The value of π For any circle the circumference is always just over three times bigger than the radius. The exact number is called π (pi). We use the symbol π because the number cannot be written exactly. π = 3.141592653589793238462643383279502884197169 39937510582097494459230781640628620899862803482 53421170679821480865132823066470938446095505822 31725359408128481117450284102701938521105559644 62294895493038196 (to 200 decimal places)! Explain that pi is just a number. We call it pi because it is not possible to write the number exactly. Even written to 200 decimal places, although extremely accurate, is an approximation.

Approximations for the value of π When we are doing calculations involving the value π we have to use an approximation for the value. For a rough approximation we can use 3. Better approximations are 3.14 or . 22 7 We can also use the π button on a calculator. Most questions will tell you what approximations to use. It is useful to approximate pi to a value of 3 when approximating the answers to calculations. When a calculation has lots of steps we write π as a symbol throughout and evaluate it at the end, if necessary.

The circumference of a circle For any circle, π = circumference diameter or, π = C d We can rearrange this to make a formula to find the circumference of a circle given its diameter. Pupils should be asked to learn these formulae. C = πd

The circumference of a circle Use π = 3.14 to find the circumference of this circle. C = πd 8 cm = 3.14 × 8 = 25.12 cm Tell pupils that when solving a problem like this they should always start by writing down the formula that they are using. This will minimize the risk of using the radius instead of the diameter, for example.

Finding the circumference given the radius The diameter of a circle is two times its radius, or d = 2r We can substitute this into the formula C = πd to give us a formula to find the circumference of a circle given its radius. C = 2πr

The circumference of a circle Use π = 3.14 to find the circumference of the following circles: 4 cm 9 m C = πd C = 2πr = 3.14 × 4 = 2 × 3.14 × 9 = 12.56 cm = 56.52 m 23 mm For each one, start by asking pupils what formula we have to use. Estimate each answer first using  = 3, or use this to check the answer. 58 cm C = πd C = 2πr = 3.14 × 23 = 2 × 3.14 × 58 = 72.22 mm = 364.24 cm

Finding the radius given the circumference Use π = 3.14 to find the radius of this circle. C = 2πr 12 cm How can we rearrange this to make r the subject of the formula? C 2π r = ? Link: A3 Formulae – changing the subject of a formula 12 2 × 3.14 = = 1.91 cm (to 2 d.p.)

Circumference problem The diameter of a bicycle wheel is 50 cm. How many complete rotations does it make over a distance of 1 km? Using C = πd and π = 3.14, The circumference of the wheel = 3.14 × 50 = 157 cm 1 km = 100 000 cm Explain that we can ignore any remainder when dividing 100000 by 157 because we are asked for the number of complete rotations. 50 cm The number of complete rotations = 100 000 ÷ 157 = 637

Circumference of a Circle The Circumference of a circle can be calculated using the formulae: C = 2πr or C = πd Where d is the diameter, r is the radius and π = 3.14 to 2 decimal places Circles 1 #s 1a-e, 3a-e, 5, 6 & 9aef