You have purchased a scale model of a car. The scale factor is 1:24. The model is 2.9 inches high, 2.75 inches wide, and 6.4 inches long.
Find the dimensions of the car in feet.
If the rear cargo area of the actual car has a volume of 12.5 cubic feet, what is the volume of the rear cargo area of the model?
How would you set it up to find the answer?
Multiply each dimension by 24 to get dimensions in inches, then divide by 12 to get answers in feet.
For cargo area, reverse the process.
To find the dimensions of the car in feet, we need to use the scale factor of 1:24. This means that every 1 unit on the model represents 24 units in the actual car.
For the height, we can multiply the height of the model (2.9 inches) by the scale factor (24) and then convert it to feet by dividing by 12 (since there are 12 inches in a foot):
Height of the car in feet = (2.9 inches * 24) / 12 = 5.8 feet
Similarly, we can find the width and length:
Width of the car in feet = (2.75 inches * 24) / 12 = 5.5 feet
Length of the car in feet = (6.4 inches * 24) / 12 = 12.8 feet
To find the volume of the rear cargo area in the model, we can use the same scale factor. Since volume is measured in cubic units, we need to apply the scale factor cubed (24^3):
Volume of the rear cargo area of the model = (Volume of the actual car) / (Scale factor^3)
Volume of the rear cargo area of the model = 12.5 cubic feet / (24^3)
Calculating this value, we get the volume of the rear cargo area in the model.