the volume of a 1968 ford mustang gt engine is 390 cubic inches. which scale model of the mustang has the greater engine volume, a 1:18 scale model or a 1:24 scale model? how much greater is it?
the volumes of the model engines are proportional to the cubes of the scale factors
To determine which scale model of the Mustang has the greater engine volume, we need to compare the volumes of the two scale models.
Let's start by calculating the volume of the engine in each scale model.
1. 1:18 scale model:
The scale 1:18 indicates that every unit on the model represents 18 units in real life.
So, the volume of the engine in the 1:18 scale model would be: 390 cubic inches * 18^3.
2. 1:24 scale model:
Similarly, the scale 1:24 indicates that every unit on the model represents 24 units in real life.
So, the volume of the engine in the 1:24 scale model would be: 390 cubic inches * 24^3.
Now, we can compare the two volumes and determine which scale model has the greater engine volume:
If the volume of the engine in the 1:18 scale model is greater, we can calculate the difference as follows:
Difference = Volume of 1:18 scale model - Volume of 1:24 scale model.
On the other hand, if the volume of the engine in the 1:24 scale model is greater, we can calculate the difference as follows:
Difference = Volume of 1:24 scale model - Volume of 1:18 scale model.
By performing the calculations, we can determine which scale model has the greater engine volume and the value of the difference.
To determine which scale model of the Mustang has the greater engine volume, we need to compare the volumes of the engines in both models.
First, let's calculate the volume of the real engine in the 1968 Ford Mustang GT, which is given as 390 cubic inches.
Now, let's consider the two scale models: 1:18 and 1:24. This means that for every 1 inch on the model, it represents 18 inches and 24 inches on the actual car, respectively.
To find the volume of the model engines, we need to take the cube of the scale ratio since volume is calculated in cubic units. Therefore, for the 1:18 scale model, the scale ratio is 18, and for the 1:24 scale model, the scale ratio is 24.
For the 1:18 scale model:
Volume of model engine = (Volume of real engine) * (Scale ratio)^3
Volume of model engine = 390 in^3 * (18)^3
For the 1:24 scale model:
Volume of model engine = (Volume of real engine) * (Scale ratio)^3
Volume of model engine = 390 in^3 * (24)^3
Now we can calculate the volumes of the engines for both scale models and compare them to determine which is greater. After that, we can find out how much greater it is by subtracting the smaller volume from the larger volume.
Let me calculate that for you.