Interpolation, non linear. Need help please.

Greetings. I am calculating gallons for a wine tank. I've done all the numbers and I know the total gallons, but I need to chart the gallons-per-inch in the cone part of the tank.

The cone is 32inch radius at the bottom, 9inch radius at top. It is 12" high. I've calculated that it holds 84 gallons, but I need to show this exponent over 12 cells in Excel.

I don't know what to do. I've never used logest or growth or an exponent function. I've kept it simple up until now.

here is a screen shot. The neck of the tank is 1.01 gallons per inch, and beneath the cone is the body which is 15.72 gallons per inch.

Thank you for any help



Tank dip.jpg

I think the OP has the volume figured out. I think he's asking how to scale the 1 inch points of the cone in exponential units.

I've come up with this, but please check my calcs.

conical_section.jpg

From this we get that the height of the cone from (truncated) apex to the 9" radius point is 4.696", and to the 32" radius point is 16.696 inches. So strategy is to simply calculate full cone volume from the apex to each 1-inch dip marker, and then subtract the volume of the 4.696" high truncated cone.

conical_section_cy.xlsx

And completing your dip table:

conical_dip_table.jpg

But there's definitely something wrong with the size of the change between Dip 16 and 17. Either there's still something I'm missing in my calcs, or the initial Gallon value in 17 is wrong. Please can you verify this?

Formula:

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Man, you all are crazy talented. Yeah two of you mentioned how my tank was off by one inch. That is what I might call 'winery brain'... It's just that simple inversion when your measuring tape reads 12" that the tank is more full than if the tape read 12.5"... So I probably need to go over the rest of the chart. My volumes, outside of the cone, are good, and the winery I work at was off by 3.5 barrels (210 gallons) the last time they pumped into the tank, so this is infinitely more accurate.
Thank you so much for the help. I was thinking about completing the triangle as well, to help visualize the cone, but then I started drinking wine.