If the volumes of two solid is in a certain ratio, we can often find relationships between some lengths of the solids even if the solids are not similar. Suppose the volume of the cylinder and sphere below are in the ratio 2:3. The radius of the sphere is twice the radius of the cylinder, […]

## Volumes of Frustums

A frustum is that past of a pyramid or cone that lines between two parallel planes cutting it. If one of the planes is the base and the other is horizontal then the result is the shape shown below right (for a cone). The smaller cone top right and the original cone left are similar […]

## Density of a Mixture Made of Substances in a Certain Ratio

Substances are often combined to make new substances. Metal alloys are made by mixing metals together in certain proportions to give certain properties of strength, hardness, density or some other quality. If it is required that the density be a certain value then we can calculate the proportions in which the metals should be combined […]

## Units, Conversion Factors and Constants

Distance is usually measured in metres, m, but can also be measured in centimetres, cm, millimetres, mm, kilometres, km or miles. 1 mile=1.609 km (often approximated to 1.6) = 1609 metres (often approximated to 1600) = 160900 cm = 1609000 mm Speed is usually measured in metres per second, m/s, or kilometres per hour, km/h, […]

## Volume

A prism is a shape with a constant cross section, in other words the cross-section looks the same anywhere along the length of the solid (examples: cylinder, cuboid). The volume of a prism = the area of the cross-section × the length. So, for example, the volume of a cylinder area of a triangle = […]