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.

Question

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.

ash2326 · Answer

Take two similar cuboids, let the first one have  the dimensions $4\times 6\times 8$
Now the ratio between the two (you can choose any), let it be 1/2
Now can you tell me the dimensions of the second cuboid

sarahc · Answer

can it be anything?

ash2326 · Answer

nope, we chose the ratio as 1:2.  and we have the dimensions of the first cuboid. Now use it to find the dimensions

sarahc · Answer

2x3x4? idk...so lost.

ash2326 · Answer

the ratio is 1:2
let the length of the second be L
and we have the first cuboid's length as 4, so
$$\frac 4 L=\frac 12$$
Now you can find the length from this, similarly find other dimensions, ratio would be the same for all.
Do you get this?

sarahc · Answer

okay so 8?

ash2326 · Answer

yeah, correct. Now find the other two dimensions

sarahc · Answer

how? sorry :?

ash2326 · Answer

the same way as we found length, 
use the first one's width, you have the ratio and find the second cuboid's width

sarahc · Answer

I have a feeling I'm making this seem harder than it really is..

ash2326 · Answer

it's easy, i'll show you once more
width of first one 6
let the width of second be w
and we have the ratio as 1/2 so
$$\frac 6 w=\frac 12$$
now find w from here:)

sarahc · Answer

12..

ash2326 · Answer

Yeah, now find the height:)

sarahc · Answer

16

ash2326 · Answer

good :D
Did you understand till here?

sarahc · Answer

okay so that would be the demotions of the other one?

sarahc · Answer

Lol I'm half asleep, sorry

sarahc · Answer

dimensions

ash2326 · Answer

no worries, you should sleep now. I'll help when you are awake

ash2326 · Answer

yeah the dimensions of the other cuboid, the two cuboids are similar with a similarity ratio of 1/2

sarahc · Answer

Okay :) the ratio of their surface area and volume? :o

ash2326 · Answer

@sarahc I gotta bounce now, Sorry
my friends @lgbasallote @apoorvk will help you out

sarahc · Answer

okay...thanks for your help !