Video: Finding the Scaled Height of a Tower given its Actual Height and a Scale of Modeling

An engineer makes a model of a 600-meter-tall tower to a scale of 1 : 750. What is the model’s height in centimeters?

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Video Transcript

An engineer makes a model of a 600-meter-tall tower to a scale of one to 750. What is the model’s height in centimeters?

So if we think about the model the engineer’s made, well, we know that the scale is one to 750. And we know that the real height is 600 meters. However, we don’t know the height of our model. But what we do know from the scale is that one meter on our model is worth 750 meters in real life. Well, if we think about the scale factor — well, in this case, the scale factor is 750 — then what we know is that the scale factor is equal to the real length over the model length. So therefore, if we want to find the model length, this is gonna be equal to the real length divided by the scale factor.

So therefore, in our example, it’s a model height that we’re looking at. So the model height is gonna be equal to the real height, which is 600 meters, divided by the scale factor, which is 750, which is gonna be equal to 0.8 meters. Well, we know that one meter is equal to 100 centimeters, so therefore we could write this as 80 centimeters. So we know that the model’s height in centimeters is 80. And we’ve given it in centimeters because that was what was asked for in the question.

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