MHB Height/diameter relationship of 19 (H8/D8=19)

[nelg]

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]

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

 

[nelg]

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

:DNelg