Question

A scale model of an airplane is 45 centimeters long. The length of the actual airplane is 30 meters long. Part A which statement about the scale for the model airplane is true?

1. The scale is 2 centimeters equal 3 meters. 2. The scale is 3 centimeters equal 2 meters.

3. The scale is 3 centimeters equal to 5 meters.

4. The scale is 5 centimeters equal to 3 meters.

Part B the total width of the actual airplane is 24 meters what is the total width of the scale model in centimeters?

Answer 1

Part A:

To determine the scale of the model airplane, we need to compare the length of the model to the length of the actual airplane. We can set up a proportion:

model length / actual length = scale factor

Plugging in the given values, we get:

45 cm / 30,000 cm = scale factor

Simplifying the fraction by dividing both numerator and denominator by 15, we get:

3 cm / 2000 cm = scale factor

We can simplify this fraction further by dividing both numerator and denominator by 3:

1 cm / 667 cm = scale factor

This means that 1 centimeter on the model airplane represents 667 centimeters (or 6.67 meters) on the actual airplane.

Therefore, the correct statement about the scale for the model airplane is:

Option 4. The scale is 5 centimeters equal to 3 meters.

Part B:

To find the width of the scale model, we need to use the same scale factor we found in part A. We know that the actual width of the airplane is 24 meters, so we can set up a proportion:

model width / actual width = scale factor

Plugging in the values we know, we get:

model width / 24 m = 1 cm / 667 cm

Solving for the model width, we get:

model width = (24 m x 1 cm) / (667 cm)

model width = 0.036 m

We need to convert meters to centimeters to get the answer in centimeters:

model width = 0.036 m x 100 cm/m

model width = 3.6 cm

Therefore, the total width of the scale model is 3.6 centimeters.