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height/diameter relationship of 19 (H8/D8=19)

nelg

New member
Oct 29, 2019
2
Hi and thanks for your help in advance Math Help Board Members,

I have this quote:
"The extractor of the 0.1L unit has a volume of 100mL and an internal height/diameter relationship of 19 (H8/D8=19)"

Sorry to sound so silly, but can someone please help me work with this equation?
I would like a cylinder that would hold approximately 5.0L.
What should the Height and Diameter be?

Cheers

🍻 Nelg
 

HallsofIvy

Well-known member
MHB Math Helper
Jan 29, 2012
1,151
The area of a circle of radius r is \(\displaystyle \pi r^2\). Since the radius is 1/2 the diameter, r= d/2, \(\displaystyle r^2= d^2/4\) so we can write that as \(\displaystyle \pi d^2/4\). A cylinder or diameter d and height h has volume \(\displaystyle \pi d^2h/4\). So we want \(\displaystyle H_8\) and \(\displaystyle D_8\) that satisfy \(\displaystyle \pi D_8^2H_8/4= 5\).
If we also want "an internal height/diameter relationship of \(\displaystyle 19 (H_8/D_8=19)\)" then [tex]H_8= 19D_8[/tex] and \(\displaystyle \pi D_8(19D_8)/4= \frac{19\pi}{4}D_8^2= 5\) so \(\displaystyle D_8^2= \frac{20}{19\pi}\).
 

nelg

New member
Oct 29, 2019
2
WOW...thanks HallsofIvy!
I'm going to need some time to digest your work.
I am in complete awe and thanks! :D

I'm currently trying to create an Excel spreadsheet that will 'spit out' the volume of the cylinder based on H/D=19 relationship.

This could take me a while...I'll keep you posted

:D


Nelg