Question

Looking for someone who can work this out with me! I'm not looking for an answer, just help!!
Part 1: Create and provide the dimensions for two similar figures of your choosing.
Part 2: What is the similarity ratio of these figures along with the ratio of their surface area and volume?
Part 3: Show your work, either using the actual volumes or using the formula, that the volume ratio is true.

Answer 1

So far I made 2 similar equilateral cubes. One of them with the dimensions 9, 9, 9 and the other one with dimensions 27, 27, 27.

Answer 2

9, 9, 9 Volume = 729^3
27, 27, 27 Volume = 19, 683^3
9, 9, 9 Surface Area = 486^2
27, 27, 27 Surface Area= 4,374^2

Answer 3

Now how do I put this information (if it is right) into ratio form?

Answer 4

What is the similarity ratio of these figures?

ratio can be written as a fraction. in this case the similarity ratio is
\[ \frac{9}{27} = \frac{1}{3} \]
or it could be written as 1:3 (read as "one is to 3")
do the same for the areas and volumes. If you did everything correctly, the areas should be in ratio 1:9 (1 to 3^2)
and volume is 1:27 (1 to 3^3)

Answer 5

btw, I would not write the answers as
9, 9, 9 Volume = 729^3 (because 729^3 means 729*729*729)
the volume is 9*9*9 = 729 (cubic units (example cubic inches if you started with 9 inches for each side)

9*9*9= 9^3 (9^3 is just a short-cut for 9*9*9 )
and 9^3 = 729

Answer 6

Thank you so much. :D I almost put that too.