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

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The discussion centers on calculating the height and diameter of a cylinder with a volume of approximately 5.0L while maintaining a height/diameter ratio of 19. The formula for the volume of a cylinder is provided, leading to the equation that incorporates the desired ratio. The calculations reveal that the diameter squared equals 20 divided by 19 times pi. The user expresses gratitude for the assistance and plans to create an Excel spreadsheet to automate future calculations based on the height/diameter relationship. The conversation emphasizes the importance of understanding geometric relationships in practical applications.
nelg
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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
 
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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].
 
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
 
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