SOLUTION: The corresponding edges of two similar triangular prisms are in the ratio 3:5. What is the ratio of their surface areas? What is the ratio of their volumes?

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Question 149520: The corresponding edges of two similar triangular prisms are in the ratio 3:5. What is the ratio of their surface areas? What is the ratio of their volumes?

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
If you know the ratio of two corresponding sides of two figures, then you can find the ratio of the surface area and volume


Since the ratio of the two corresponding sides is 3:5, this means that edge_prism_1%2Fedge_prism_2=3%2F5


So the ratio of the two surface areas is simply the square of the ratio of the two sides. This means that ratio of the two surface areas is simply

3%5E2%2F5%5E2=9%2F25

Consequently, this works with volume also. So ratio of the two volumes is:

3%5E3%2F5%5E3=27%2F125



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If it's too simple to believe, then try this:

Let's say we have a rectangle with dimensions with a length of 2 and a width 1. Also, we have another rectangle with a length of 4 and a width 2. Note: the two figures must be similar.



So we can see that the ratio of the sides is 4:2 or 2:1. Now let's find the two areas

Rectangle 1
A=2%2A1=2

Rectangle 2
A=4%2A2=8


So the ratio of the areas is 8:2 or 4:1

Notice how 4:1 is simply the result of squaring 2:1


This concept is analogous in 3 dimensions also.


Let me know if need more examples.