You are designing a scale model of the solar system mercury it is 4,878 km in diameter.using the following scale factor, how large does your model of mercury need to be?
A. 160cm
B. 16cm
C.146cm
D.30cm
You forgot to post the scale factor.
16
To determine the size of the scale model of Mercury, you need to calculate the scaled diameter using the given scale factor.
The scale factor is the ratio of the diameter of the model to the actual diameter of Mercury.
Let's calculate the scaled diameter using each option:
A. 160cm:
Scaled Diameter = Actual Diameter x Scale Factor
Scaled Diameter = 4,878 km x Scale Factor
Setting up the equation:
160 cm = 4,878 km x Scale Factor
Scale Factor = 160 cm / 4,878 km
Converting cm to km:
Scale Factor = 160 cm / (4,878 km * 100,000 cm/km)
Scale Factor ≈ 3.27 x 10^-4
B. 16cm:
Scaled Diameter = Actual Diameter x Scale Factor
Scaled Diameter = 4,878 km x Scale Factor
Setting up the equation:
16 cm = 4,878 km x Scale Factor
Scale Factor = 16 cm / 4,878 km
Converting cm to km:
Scale Factor = 16 cm / (4,878 km * 100,000 cm/km)
Scale Factor ≈ 3.27 x 10^-5
C. 146cm:
Scaled Diameter = Actual Diameter x Scale Factor
Scaled Diameter = 4,878 km x Scale Factor
Setting up the equation:
146 cm = 4,878 km x Scale Factor
Scale Factor = 146 cm / 4,878 km
Converting cm to km:
Scale Factor = 146 cm / (4,878 km * 100,000 cm/km)
Scale Factor ≈ 2.99 x 10^-4
D. 30cm:
Scaled Diameter = Actual Diameter x Scale Factor
Scaled Diameter = 4,878 km x Scale Factor
Setting up the equation:
30 cm = 4,878 km x Scale Factor
Scale Factor = 30 cm / 4,878 km
Converting cm to km:
Scale Factor = 30 cm / (4,878 km * 100,000 cm/km)
Scale Factor ≈ 6.13 x 10^-5
Based on the calculations, the correct answer would be B. 16cm, as it results in the closest approximation to the actual scale factor.
To determine the size that the model of Mercury needs to be, we need to use the given scale factor. The scale factor relates the dimensions of the actual object to the dimensions of the model.
In this case, we have the diameter of Mercury, which is 4,878 km. Let's assume the scale factor is x.
To find the size of the model, we can set up a proportion:
Actual diameter / Model diameter = Scale factor
Using the given information:
4878 km / Model diameter = x
Now, we need to rearrange the equation to solve for the model diameter:
Model diameter = 4878 km / x
Let's substitute each given choice for x to see which one gives us the correct model diameter:
A. Model diameter = 4878 km / 160 cm
B. Model diameter = 4878 km / 16 cm
C. Model diameter = 4878 km / 146 cm
D. Model diameter = 4878 km / 30 cm
To get the answer, we need to convert km to cm:
1 km = 100,000 cm
Therefore, the correct calculation is:
Model diameter = 4878 km * 100,000 cm / x
Let's calculate the model diameter for each choice:
A. Model diameter = (4878 km * 100,000 cm) / 160 cm = 3,048,750 cm
B. Model diameter = (4878 km * 100,000 cm) / 16 cm = 30,487,500 cm
C. Model diameter = (4878 km * 100,000 cm) / 146 cm = 3,343,836 cm
D. Model diameter = (4878 km * 100,000 cm) / 30 cm = 16,260,000 cm
Comparing the calculated values with the given choices, we can see that the correct answer is:
B. 16 cm
Thus, the model of Mercury needs to be 16 cm in diameter according to the given scale factor.