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

#### nelg

##### New member
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)"

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
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 $$H_8= 19D_8$$ 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
WOW...thanks HallsofIvy!
I'm going to need some time to digest your work.
I am in complete awe and thanks! 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 Nelg