Answer :
The dimensions of his model of the train station would be
3 inches by 6 inches by 4 inches.
What is scale factor?
Scale factor is a dimensionless constant value that is used to compare the size of two objects. It is denoted by [K]. Mathematically -
K = O[1]/O[2]
Given is Lewis who is building a train layout and wants to build a model of the train station in his city. He wants it to be exactly to scale to match his engine. The engine measures 8 inches long and is the model of a train that is 80 feet long. The station in his city is 30 feet by 60 feet by 40 feet.
Now, it is given here that Lewis assumed a dilation model in which 80 feet is 8 inches long. Then -
80 feet = 8 inches
So one feet will be -
1 ft = 8/80 = 1/10 inches
Now, the dimensions of station in Lewis native city is 30 feet by 60 feet by 40 feet.
Now, dilating the dimensions with a scale factor of 1/10 inches, we get -
30 feet = 30 x 1 feet = 30 x 1/10 = 3 inches
60 feet = 60 x 1 feet = 60 x 1/10 = 6 inches
40 feet = 40 x 1 feet = 40 x 1/10 = 4 inches
Therefore, the dimensions of his model of the train station would be
3 inches by 6 inches by 4 inches.
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https://brainly.com/question/20297060
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