Answer:
[tex]Ratio = \frac{1}{16}[/tex] ----- Model length to Actual length
[tex]Ratio = \frac{1}{256}[/tex] ----- Model Area to Actual Area
Explanation:
Given
Model Measurement:
[tex]Length = \frac{1}{2}\ in[/tex]
[tex]Width = \frac{1}{6}\ in[/tex]
Actual Measurement:
[tex]Length = \frac{2}{3}\ ft[/tex]
[tex]Width = \frac{2}{9}\ ft[/tex]
Solving (a): Ratio of actual length to model length
Convert length from feet to inches
[tex]Length = \frac{2}{3}\ ft[/tex]
[tex]Length = \frac{2}{3}\ * 12in[/tex]
[tex]Length = \frac{24\ in}{3}[/tex]
[tex]Length = 8\ in[/tex]
The required ratio is calculated by dividing the model length by the actual length
[tex]Ratio = \frac{Model}{Actual}[/tex]
[tex]Ratio = \frac{1}{2}\ in/8\ in[/tex]
[tex]Ratio = \frac{1}{2}/8[/tex]
[tex]Ratio = \frac{1}{2} * \frac{1}{8}[/tex]
[tex]Ratio = \frac{1}{16}[/tex]
Another possible way is to convert both measurement to a different unit:
Convert model length from inches to cm
[tex]Length = \frac{1}{2}\ in[/tex]
[tex]Model\ Length = \frac{1}{2} * 2.54cm[/tex]
[tex]Model\ Length = \frac{1 * 2.54cm}{2}[/tex]
[tex]Model\ Length = \frac{2.54cm}{2}[/tex]
[tex]Model\ Length = 1.27 cm[/tex]
Convert actual length from ft to cm
[tex]Length = \frac{2}{3}\ ft[/tex]
[tex]Actual\ Length = \frac{2}{3} * 30.48cm[/tex]
[tex]Actual\ Length = \frac{2 * 30.48cm}{3}[/tex]
[tex]Actual\ Length = \frac{60.96cm}{3}[/tex]
[tex]Actual\ Length = 20.32cm[/tex]
Then calculate the ratio as:
[tex]Ratio = \frac{Model}{Actual}[/tex]
[tex]Ratio = \frac{1.27cm}{20.32cm}[/tex]
[tex]Ratio = \frac{1.27}{20.32}[/tex]
Simplify fraction
[tex]Ratio = \frac{1.27/1.27}{20.32/1.27}[/tex]
[tex]Ratio = \frac{1}{16}[/tex]
Solving (b): Model of Area;
Way 1:
In (a), we calculated the ratio of length to be:
[tex]Ratio = \frac{1}{16}[/tex]
This is also the model of the width.
So, Ratio of Area is then calculated as:
[tex]Ratio = \frac{1}{16}^2[/tex]
[tex]Ratio = \frac{1}{256}[/tex]
Way (2): We calculate the actual area of the model and actual measurements.
Model Measurements
[tex]Length = \frac{1}{2}\ in[/tex]
[tex]Width = \frac{1}{6}\ in[/tex]
[tex]Area = Length * Width[/tex]
[tex]Area = \frac{1}{2} * \frac{1}{6} in^2[/tex]
[tex]Area = \frac{1}{12}\ in^2[/tex]
Actual Measurements
[tex]Length = \frac{2}{3}\ ft[/tex]
[tex]Width = \frac{2}{9}\ ft[/tex]
[tex]Area = Length * Width[/tex]
[tex]Area = \frac{2}{3} * \frac{2}{9} ft^2[/tex]
[tex]Area = \frac{4}{27} ft^2[/tex]
Convert to [tex]in^2[/tex]
[tex]Area = \frac{4}{27} * 144in^2[/tex]
[tex]Area = \frac{4}{3} * 16in^2[/tex]
[tex]Area = \frac{64}{3}in^2[/tex]
Ratio is then calculated as:
[tex]Ratio = \frac{Model}{Actual}[/tex]
[tex]Ratio = \frac{1}{12}/\frac{64}{3}[/tex]
[tex]Ratio = \frac{1}{12} * \frac{3}{64}[/tex]
[tex]Ratio = \frac{1}{4} * \frac{1}{64}[/tex]
[tex]Ratio = \frac{1}{256}[/tex]
