Circles Shape and Space

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 = (to 200 decimal places)!

Approximations for the value of π When we are doing calculations involving the value π we have to use an approximation for the value. Generally, we use the approximation 3.14 We can also use the π button on a calculator. 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, We can rearrange this to make a formula to find the circumference of a circle given its diameter. C = πd π = C d

Circle circumference and diameter

The circumference of a circle Use π = 3.14 to find the circumference of this circle. C = πd 8 cm = 3.14 × 8 = cm

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

The circumference of a circle Use π = 3.14 to find the circumference of the following circles: C = πd 4 cm = 3.14 × 4 = cm C = 2 πr 9 m = 2 × 3.14 × 9 = m C = πd 23 mm = 3.14 × 23 = mm C = 2 πr 58 cm = 2 × 3.14 × 58 = cm

? Finding the radius given the circumference Use π = 3.14 to find the radius of this circle. C = 2 πr 12 cm How can we rearrange this to make r the subject of the formula? r = C 2π2π 12 2 × 3.14 = = 1.91 cm (to 2 d.p.)

Find the perimeter of this shape Use π = 3.14 to find perimeter of this shape. The perimeter of this shape is made up of the circumference of a circle of diameter 13 cm and two lines of length 6 cm. 6 cm 13 cm Perimeter = 3.14 × = cm

Circumference problem The diameter of a bicycle wheel is 50 cm. How many complete rotations does it make over a distance of 1 km? 50 cm The circumference of the wheel = 3.14 × 50 Using C = πd and π = 3.14, = 157 cm The number of complete rotations = ÷ 157 = km = cm

Formula for the area of a circle We can find the area of a circle using the formula radius Area of a circle = πr 2 Area of a circle = π × r × r or

Area of a circle

The circumference of a circle Use π = 3.14 to find the area of this circle. A = πr 2 4 cm = 3.14 × 4 × 4 = cm 2

Finding the area given the diameter The radius of a circle is half of its radius, or We can substitute this into the formula A = πr 2 to give us a formula to find the area of a circle given its diameter. r = d 2 A = πd2πd2 4

The area of a circle Use π = 3.14 to find the area of the following circles: A = πr 2 2 cm = 3.14 × 2 2 = cm 2 A = πr 2 10 m = 3.14 × 5 2 = 78.5 m 2 A = πr 2 23 mm = 3.14 × 23 2 = mm 2 A = πr 2 78 cm = 3.14 × 39 2 = cm 2

Find the area of this shape Use π = 3.14 to find area of this shape. The area of this shape is made up of the area of a circle of diameter 13 cm and the area of a rectangle of width 6 cm and length 13 cm. 6 cm 13 cm Area of circle = 3.14 × = cm 2 Area of rectangle = 6 × 13 = 78 cm 2 Total area = = cm 2