Geometry

The Circle

The Circle

Pi is symbolised by ? and is a magical number which is used to find the circumference of a circle and the area of a circle.

Pi is a value just bigger than 3 and the phrase:

“How I wish I could recollect pi”

Allows us to recall pi to six decimal places by counting the numbers of letters in each word:

3 – 1 – 4 – 1 – 5 – 9 – 2

Given to three decimal places, pi can be rounded to 3.142

Key terms:

CaptureThe red line is the circumference.

Circumference of a Circle

This is the distance around the outside of a circle.

Capture

r = 5m

d = 2 x 5m

d= 10m

c = ?d

c = ? x 10

c = 31.4m (1 d.p.)

Sometimes we may be given the circumference and asked to find the radius:

e.g. the circumference of a circle is 100 metres. Find its radius.

Capture

c = ?d

c = 2?r (since d = 2r)

100 = 2 x ? x r

(2) (2)

50 = ? x r

(?) (?)

r = 50

?

r = 15.91549…

r = 15.9m (1 d.p.)

Area of a Circle

A = ? x r x r

A = ?r2

Capture

A = ?r2

A = ? x 10 x 10

A = ? x 100

A = 314.1592654…

A = 314.2m2 (1 d.p.)

Solutions in terms of ?

Sometimes we may be asked to leave ? in our answers. e.g. Find

  1. the circumference and
  2. the area

of the circle below, leaving pi in your answer.

Capture

c = ?d

c = ? x 2 x 7

c = 14? m

A = ?r2

We square the radius first then multiply by ? (BIDMAS)

A = ? x 72

A = 49? m2