## Circles, Cylinders, Cones and Spheres

Many designers, manufacturers, artists, engineers and people in all walks of life use circles in their work.

It is useful to know the names given to parts of a circle and about the measurement of circles.

### Parts of a Circle

 A circumference is the distance around a circle. A radius is the distance from the centre to any point on the circumference. A diameter is a chord that passes through the centre. The length of the diameter is twice the length of the radius. d = 2 × r A segment of a circle is a line from one side of a circle to the other which does NOT pass through the centre. A semi-circle is half of a full circle. The Millennium Wheel in London has the following measurements: Diameter = 135 metres Radius = 67.5 metres Circumference = 424 metres

### Pi

 π, the Greek letter pi, is a special number often used in calculations involving circles.The diameter of a circle, if wrapped around the outside of the circle, would fit just over three times (π times). If the circumference of any circle is divided by its diameter the answer is just over 3. A more exact value of π is approximately 3.14 (to 2 d.p.).The fraction with the closest value to pi is 22⁄7 or 31⁄7 Calculators and computers can work out PI to a huge number of decimal places. π = 3.141592653589793238462633832 Another kind of pie!

### Perimeter of a Circle

The perimeter of a circle is called the circumference.
The length of the circumference (C)

 C = 2 × π × r = π × d

### Area of a Circle

The area of a circle is given by the formula:

 A = π × r 2

The next three sections contain formulae for volumes of cylinders, cones and spheres which you may need for more advanced calculations.

Cylinders

cylinder is solid three dimensional object with a circlular cross section. Examples of objects which are in the shape of a cylinder include pencils, pipes and cans.

 The volume of a cylinder = shaded area x h = π r 2 h

### Cones

cone is an object with a circular or curved base. The cone tapers from the base to a fixed point. Examples of objects which are in the shape of a cone include ice-creams, clowns hats and megaphones.

 V = 1⁄3 × (area of base) × h = 1⁄3π r2 h

### Spheres

sphere is an object in the shape of a circular ball. Every point on its surface is the same distance from the centre. Examples of objects which are in the shape of a sphere include soccer balls, globes,

 The volume of a sphere = 4/3 π r3