change both measurements to the same unit of measure,and find the scale factor.
1. 4in. model of a 6ft.cabinet
2. 4cm. model of a 2m. door.
3. 12ft. model of a 100yd. playground
4. 20m. model of a 3km. street.
4 in. = 1/3 foot or 6 ft. = 72 in.
2 m = 200 cm
100 yd. = 300 ft.
3 km = 3,000 m
To find the scale factor for each of these measurements, we need to convert both measurements to the same unit of measure and then divide the model measurement by the actual measurement.
Let's tackle each example one by one:
1. 4in. model of a 6ft. cabinet:
To convert 6ft. to inches, we multiply by 12 (since there are 12 inches in a foot): 6ft. * 12in/ft. = 72in.
So the model measurement becomes 4in. while the actual measurement becomes 72in.
The scale factor is then calculated as the model measurement divided by the actual measurement: 4in. / 72in. ≈ 0.056.
2. 4cm. model of a 2m. door:
No conversion is needed here since both measurements are already in meters.
The model measurement remains 4cm while the actual measurement becomes 2m.
The scale factor is then calculated as the model measurement divided by the actual measurement: 4cm / 2m = 0.02.
3. 12ft. model of a 100yd. playground:
To convert 100yd. to feet, we multiply by 3 (since there are 3 feet in a yard): 100yd. * 3ft/yd. = 300ft.
So the model measurement becomes 12ft. while the actual measurement becomes 300ft.
The scale factor is then calculated as the model measurement divided by the actual measurement: 12ft. / 300ft. = 0.04.
4. 20m. model of a 3km. street:
To convert 3km. to meters, we multiply by 1000 (since there are 1000 meters in a kilometer): 3km. * 1000m/km. = 3000m.
So the model measurement remains 20m while the actual measurement becomes 3000m.
The scale factor is then calculated as the model measurement divided by the actual measurement: 20m / 3000m = 0.0067.
Here are the scale factors for each example:
1. Scale factor for a 4in. model of a 6ft. cabinet is approximately 0.056.
2. Scale factor for a 4cm model of a 2m. door is 0.02.
3. Scale factor for a 12ft. model of a 100yd. playground is 0.04.
4. Scale factor for a 20m. model of a 3km. street is approximately 0.0067.