Learn about Scale Drawings and Models
In this lesson let’s learn how we scale drawings and models. Before we attempt the two problems let’s understand what is the scale? The scale is basely a ratio between two different measurements. It is a ratio between two measurements. So a ratio can be express as a/b. That’s essentially what we do when we try and do scale problems. So let’s try problem one.
It says the scale model of a human heart is 16 feet long. So the model is one part of the ratio which is 16 feet long. It says the scale is 32:1 which means the ratio is 32/1. That’s the ratio. So the model is 16 feet and the actual size is what we need to find out. I'm going to actually rewrite this 16 because it didn’t write well. So the model length is 16 feet. The actual length is what we need to find. We are given the scale is 32/1 or 32:1.
These are equal. So what this means is 16 feet over let’s say y feet, whatever the value is equals 32/1 because these two are equivalent ratios. This is the scale which means for every 32 feet the actual size is one foot, 16 feet over y feet is the other ratio that we have. So if we cross multiply this, what do we get? 16 feet = 32 x y feet dividing both sides by 32, what do we get? This gets cancelled out, y = 16/32 feet or ½ feet. So the actual size of the human heart is half a foot.
Let’s try one more problem. This problem says that the actual length equals 0.3 mm. The model length equals 3 cm. So actual over model, this is the scale, actual length is three centimeters. This is the scale so actual over model but when we looked at the previous problem the scale we had was model over actual. So let’s write this out. So the scale that we’re looking for is the model over the actual. What is the model length, 3 cm which is 30 mm. And the actual is 0.3 mm. If I divide 30 by 0.3 we get 100/1.
So the scale is 100/1. Remember all we talk about when we talk about a scale is the ratio of two measurements which have the same units, 32:1 means the difference between the model and the actual is 32 times.
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