A ratio scale expresses the relationship between two quantities or values. It allows us to compare and represent different sizes or magnitudes of objects.
Ratio scales are written in the form , where N is a whole number. This ratio indicates that one unit on a scale represents N units in reality. For example, a scale of means that 1 unit on the scale represents 100 units in reality.
When scaling ratios, the units of measurement must be consistent. If necessary, convert between different units to maintain consistency.
Scaling ratios is important when creating maps and models. To create a map or model, we often need to shrink or enlarge real-world objects to fit within a certain space or size. Ratio scales help us maintain accurate and consistent proportions between the original object and its representation.
For example, city maps use ratio scales to represent large areas on a smaller sheet of paper. Similarly, architectural models of buildings, vehicles, or other structures use scaling ratios to create accurate, scaled-down representations of the original objects.
To determine the actual distance or size of an object using scaling ratios, we can use the following method:
Step 1: Identify the scaling ratio (e.g., ).
Step 2: Measure the distance or size on the map or model.
Step 3: Multiply the measurement by N to find the actual distance or size.
For example, if we have a map with a scale of , and we measure a distance of 3 cm between two points on the map, we can calculate the actual distance as follows:
Imagine creating a map of London, where the city’s layout is scaled down to fit on a single sheet of paper. In this example, the scale used is . This means that for every centimeter on the map, the actual distance represented is .
To illustrate how this works, let’s say we want to find the actual distance between Croydon and Forest Hill on this map. If the distance between these two locations on the map measures , we can calculate the real-world distance by multiplying the map distance by the scale factor.
(map distance) (scale factor)
Since equals , we can then convert the distance into kilometres:
Therefore, the actual distance between Croydon and Forest Hill is . Understanding and applying ratios in model making and map creation allows for accurate representation and easy interpretation of real-world distances and proportions.
In geometry, scale factors are used to describe similar shapes which have the same shape but may differ in size. When two shapes are similar, their corresponding sides are proportional, meaning their scaling ratio remains constant.
The scale factor is the ratio between the lengths of corresponding sides in similar shapes. This factor has a direct relationship with the area and volume of the shapes.
When enlarging or reducing a shape, the scale factor will affect its area and volume. For example, if a shape is enlarged by a scaling factor of 2, its area will increase by a factor of 4 (which is ), and its volume will increase by a factor of 8 (which is ).
A map is drawn to a scale of . Two cities are connected by a straight road of length 7.5 km. Calculate, in centimetres, the distance on the map between these two cities.
A map is drawn to a scale of . Find the actual distance apart, in km, of two villages which are represented on the map by the two dots 36 cm apart.
The length of a river is 1500 km. Find the length representing the river on a map of scale .
The actual distance from Brighton to Croydon is 70 km. This is represented by 2 cm on a map. Find the scale that has been used. Considering also that 1 mile is approximately 1.6 km, find the actual distance from Brighton to Croydon in miles.