In Math, a scale is used to represent the relationship between the measurement of a model to the corresponding measurement of the actual objects. Without scale, there is no use of blueprints and maps. The scale helps us to represent real-world things on paper with comparatively smaller dimensions. Scale is most commonly used in maps and blueprints used for construction and buildings.
What is Scale Drawing in Math?
The scale is defined as the ratio of the length in a drawing or model to the actual length of an object in the real world.
For example, in scale drawing, anything you draw on a paper with a size of “1” would have a size of “10” in the real world. Hence, the measurement of 150 mm on the drawing would be 1500 mm in the real world.
Scale Drawing Vs Original
Let’s now learn how to write scales in drawing.
How To Write Scales?
A ratio is used to write scales. In other words, the scale is written as the length in the drawing, then a colon (:), then the actual length. This implies that:
The scale of Drawing = Length of Drawing: Actual Length
Similarly, we have:
Map Scale= Map Distance: Actual Distance
How Is Scale Expressed?
A scale is expressed in the following two ways.
You can use units in scale such as 1 cm to 1 km.
Also, without clearly mentioning units such as 1: 100 000. (This implies that the real distance is 100 000 times the length of 1 unit on a drawing).
Let us understand with an example.
Express 5 cm to 5 m in ratio form.
5 cm to 5 m = 5 cm : 5 m
= 5 cm : 500 cm ( 1 m = 100 cm, hence 5m = 500 cm)
= 1 : 100
Simplify the scale 5 mm: 2 m.
5mm : 2 m = 5mm : 2000 mm ( 1 m = 1000 mm, hence 2 m = 2000 mm)
= 1 mm : 400 mm
= 1 : 400
Simplify the scale 5 cm: 4 km
5 cm : 4 km = 5 : 400000 cm ( 1 km = 100,000 cm, hence, 4 km = 400,000 cm)
= 1cm : 80000 cm
= 1: 80000
How To Calculate The Scales of Drawings Using a Calculator?
To calculate the scales of drawing using calculator:
Divide the measurement by the scale if you want to minimize the drawing in size, or
Multiply the measurement by the scale if you want to increase the drawing in size.
A 100 mm line is to be drawn at a scale of 1: 5.
To draw a 100 mm line at a scale of 1: 5 (i.e. 5 times less than its original size), we will divide 100 mm by 5.
= 100 mm 5
= 20 mm
Therefore, a 20 mm line is drawn.
A 100 mm line is to be drawn at a scale of 5 : 1.
To draw a 100 mm line at a scale of 5: 1 (i.e. 5 times more than its original size), we will multiply 100 mm by 5.
= 100 mm 5
= 500 mm
Therefore, a 500 mm line is drawn.
How To Interpret Scale Drawing?
We can easily interpret scale drawing if the required information is given. Let us consider an example that represents how a scale is used to prepare the blueprint of a house and how to calculate and interpret the required dimensions.
Example: To prepare the blueprint of a house, Hitesh has used a scale of 1:100. The dimensions of the master bedrooms in the floor plan are represented as 6 units by 4 units. Find the actual dimensions of the master bedroom.
Step 1: The scale 1:100 implies that for every 100 units in the real world, the house represents 1 unit on the blueprint drawing. In other words, it implies that 100 units of an actual house is equal to 1 unit of a blueprint drawing.
Step 2: Now, we will calculate the actual dimensions of the master bedroom using scale 1:100. Here, the scale factor is 100, therefore, we will multiply the blueprint dimensions by 100.
Actual length of master bedroom = 6 100 = 600 units
Actual width of master bedroom = 4 100 = 400 units
Hope you have understood what scale is, and how ratio is used to write scale in Math. With this understanding, you can now easily draw the blueprints of the original design with precise measurements.