6. Students are building a model of volcano. The volcano is about 7,992 feet tall. The students want the model to be 18 inches tall. What scale should they use?
7. Two cities on a map were 2 1/4 inches apart. The cities are actually 56.25 miles apart. What scale was used to draw the map.
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Hi, this has stumped me a lot and is there a way of working this out or is it just a one word type of answer? If you could help, I'd greatly appreciate it. Thanks!
I will do the first one, you do the 2nd in the same way
volcano : model = 7992 ft : 18 inches
= 444 ft : 1 inch
Notice I had to keep the units since they were different
if we change the ft to inches the ratio would be
5328 inches : 1 inch
now I can drop the units
volcano : model = 5328 : 1
you will have to see which answer they want
7. 56.25/2.25 = 25 mi/in.
Scale: 1 in. = 25 miles.
Hello! I'm here to help you. Don't worry, figuring out the scale can be quite straightforward once you know the formula. To find the scale, we need to divide the actual measurement by the corresponding measurement on the model.
Let's start with the first question:
6. To find the scale for the model of the volcano, we need to divide the actual height of the volcano (7,992 feet) by the desired height of the model (18 inches). This will give us the scale factor.
Scale factor = Actual Height / Model Height
In this case, the actual height is in feet and the desired height is in inches, so we need to convert the units before dividing:
7,992 feet = 7,992 * 12 inches (1 foot = 12 inches)
Model height = 18 inches
Now we can calculate the scale factor:
Scale factor = (7,992 * 12 inches) / 18 inches
Simplifying further:
Scale factor = 7,992 * 12 / 18
Scale factor = 5,328
So, the scale the students should use for their volcano model is 1:5,328. This means that every unit on the model represents 5,328 units in real life.
Now, let's move on to the second question:
7. To find the scale used to draw the map, we need to divide the actual distance between the cities (56.25 miles) by the distance between the cities on the map (2 1/4 inches).
Scale factor = Actual Distance / Map Distance
First, let's convert the mixed fraction to an improper fraction:
2 1/4 inches = (2 * 4 + 1) / 4 inches = 9/4 inches
Now we can calculate the scale factor:
Scale factor = 56.25 miles / (9/4) inches
Dividing by a fraction is the same as multiplying by its reciprocal:
Scale factor = 56.25 miles / (9/4) inches = 56.25 miles * (4/9) inches
Simplifying further:
Scale factor = 56.25 * 4 / 9
Scale factor = 25
So, the scale used to draw the map is 1:25. This means that every unit on the map represents 25 units in real life.
I hope this explanation helps you understand the process of finding the scale for these types of problems. If you have any further questions, feel free to ask!