if you have a cylinder 5 feet in diameter and 20 feet long, and you scale down the cylinder to 1 foot in diameter, how long is the cylinder?

Question

I'm having a hard time wrapping my head around this one, math isn't my strongest suit.

Answer 1

Imagine the cylinder shrinking down with all the same proportions.  We can consider these proportions:

 

new diameter       old diameter

---------------  =  ---------------  ,

 new length            old length

 

call the unknown x, and plug in

 

 1          5

---  =  ----

 x         20

 

That sets up an equation to solve, if you want the new stuff on one side and old stuff on the other side.  If you'd prefer lengths on one side and diameters on the other side, you could consider this instead:

 

new length       new diameter
-------------  =  ---------------  ,
 old length         old diameter
 
which means
 
 x         1
---  =  ---
20        5

 

Either way, you get the same answer.