Page 167 - MAT KS3 Y8 Cambridge CheckPoint

17 Area, perimeter and volume

A circle is a set of points that are all the same distance from a fixed Key words
point, called the centre.
Do you remember the names of the different parts of the circle? Make sure you learn and
understand these key words:
circumference
arc π, pi
perpendicular height
compound shape
sector

diameter

centre
chord
radius

segment
number has been given the name pi (pronounced ‘pie’) and is also known by the symbol π. π

It is a curious fact that for every circle, if you divide the length of the circumference by
the length of the diameter, you will always get the same number: 3.141592653589... This

Pi is a mathematical constant – it stands for one
Thurso
particular number. Pi has an infinitely long sequence Shetland
of numbers after the decimal point, which is why we Inverness Islands
usually use the approximation of 3.14. Aberdeen
Dundee Orkney
The existence of the constant pi means that we can use it Islands
Glasgow
in formulae about circles. In this unit you will learn two Dumfries EDINBURGH
formulae that are used with circles. Omagh Newcastle upon Tyne
Carlisle
BELFAST
The first formula, C = πd, you use to find the York
Galway Liverpool
circumference of a circle. DUBLIN Manchester
The second formula, A = πr , you use to find the area Limerick Birmingham
2
Norwich
of a circle. Cork Aberystwyth Oxford Cambridge
CARDIFF LONDON
It is thought that the number pi was used by the ancient Anglesey Bristol
Southampton
Egyptians and Babylonians in about 1900 bce. However, Exeter Brighton
Plymouth
it is the ancient Greek mathematician Archimedes of
Syracuse (287−212 bce) who is largely thought to be the
first to calculate an accurate estimation of the value of pi. You may have a π button on your
The Welsh mathematician William Jones was the first to use the calculator, but in this unit you will
Greek letter π to represent the number. Jones was born on the Isle of use a common approximation for π,
Anglesey in North Wales. In 1706 Jones published his now famous which is 3.14.
book, Synopsis palmariorum mathesios, in which the symbol π was used.
In this unit you will use the formulae for the circumference and area of a circle. You will also learn how
to work out the areas of triangles, parallelograms and trapeziums, as well as surface areas and volumes
of solid shapes.
17 Area, perimeter and volume 165