What is Scale Drawing?

In real life, we always use some measure to know the quantity, height, weight, length, or depth of anything. The word scale in math means to measure. In mathematics, scale drawing by definition means to give the exact size or measurement of the object using some standard parameter.

What is a Scale?

The scale was first invented by Anton Ullrich in 1851. Have you heard your echo? When we go to dark and big rooms we can hear our voice echoing. This would not happen when you stand in any place in the room. You need to stand at a particular distance from the wall. This is one concept in physics. But how will you know how far you have to stand to hear the echo? It would be possible if someone who heard the echo has already measured the distance at which one must stand to hear the echo. This distance can be measured using a scale.

How is Scale Drawing Used?

Suppose that your friend’s height and your height are the same. When someone asks for your height, you can tell them that you are as tall as your friend. But will that give the exact information about your height? Definitely not. Also, not everyone will know your friend. In this case, you need to provide the exact value which helps the listener to understand. This would be made easy if you use a scale or a measuring tape to calculate your height. Here, the measuring tape is considered as the scale. You can either tell your height in centimeter, inches, or any other standard unit.

Where is Scale Drawing Used?

Have you taken photocopies before? The photos will have a 2-dimensional view of your appearance. They might be taken in any ratio you want.

Any two-dimension object can be drawn on paper. This helps in easily calculating the length and width of the objects. Although the three-dimensional objects cannot be drawn as the actual figure on paper, still to some extent this drawing helps in measuring the objects.

The scale drawing helps in giving a two-dimensional representation of any place or thing.

Also, to know about a company’s loss or growth, we can make a bar chart and see the scaling. The scaled values drawn in the graph will give a quick view of the company’s progress. Thus, math plays a major role here.

Represent with Drawing

Every complex idea can be simplified by drawing. Drawing helps us to visualize the objects. To measure the height of a tall building given the angle, the actual distance of the building top from the viewer and its actual distance from the viewer standing on the ground are difficult. This involves some trigonometric calculations. But once the given information is made as a drawing, the problem is simplified. Even though the drawing might not represent the actual size, the drawing can help understand better. In this way, the length is calculated.

Scale Factor

Imagine you have invited all your friends to your birthday party and you have arranged enough juices and cakes for around 100 people. What will happen if 10 more friends come to your birthday party? You can either reduce the quantity of juice and cake meant for one person to provide for these 10 friends. Or you can order extra 10 juices and cakes to provide them. Here, you are trying the make the ratio equal either by reducing or increasing the quantity. The number by which the quantity is multiplied or divided to make the ratio equal is called the scale factor.

Can you think of some other situation in which the concept of the scale factor is involved?

Let us see some examples of the scale factor.

Suppose that you are given a map. How will you know the actual distance between two countries seeing the map? It is easy because the scale map has distance mentioned in ratios. The ratio 1:10,000 means that 1 mm (millimeter) in map equals 10,000 mm in real space.

To know the shape of microorganisms, we use a microscope. It enlarges the size of the object and helps in understanding better about the object.

Examples of Scale Drawing

Imagine that you have two large sheets of paper in your hand. Which of the two is the largest? To know this, we must know how to compare the sizes. It can be done with the help of a scale. A scale has some finite numbers from 0. Each number is at an equal distance from the adjacent numbers. The space between two numbers is divided in equal ratios. This scaling represents the actual size of the two sheets of paper helping you to know which is larger. It is measured either in inches, centimeters, or meters.

Uses of Scale Drawing

Before building a house, it is a must to plan about the rooms and the interiors. We must know how the dimension of each room like how wide a room must be. We might have noticed the overview pictures of houses for sale in the magazine and newspaper. This is called a floor plan. This will give you an idea about how spacious each room would be. If you want to add an extra room, you have to decide how to shrink the size of the other rooms to gain a new room for your house. We must have an idea about the area of the rooms for this. This work is done by architects and engineers. This is one main application of scale drawing in real life.

Can you think of some other applications of scale drawing in real life?

Practice problems

Take a scale ruler and put it on paper. Draw a hut with trees and a river beside it. When you see this scenario in reality, it would be a 3-dimensional picture. But you have made it appear 2-dimensional.

This activity is just to enrich your learning about the scale drawings.

Context and Applications  

Scale drawing is used in K-12 curriculum, undergraduate and post-graduate mathematics, and asked in entrance examinations.