# Urn volume on tapered shapes



## Buckeyepen (Nov 2, 2019)

My wife and I came home a week ago to find that my father in law finally lost his battle to cancer. We were happy to give him a good home his last three years and my wife got to see him every day which I couldn’t be more thankful for. It has come time to make an urn for him. I know about the one cubic inch per pound of weight and I have a monster articulated hollowing rig for my powermatic so I have the tools needed. My problem is the volume calculation. It is easy for a cylinder or a box but basic shapes do not catch my eye. I will want to do a tapered hollow form trick. Anyone have an idea or cheat to easier find the volume. I know I am over thinking this and head isn’t quite in it yet but it can’t be that difficult. Any help would be appreciated. I need to find size I need so I can start looking to buy some pretty wood. 

thanks.

Reactions: Sincere 6


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## gman2431 (Nov 2, 2019)

Same as you would for a cylinder except you also have to calculate the area you wont be using and subtract that. Stuff like this is best when I draw it out...

Sorry for your loss

Reactions: Thank You! 1


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## TimR (Nov 2, 2019)

I don’t remember the calculus required but I'd think a good approximation would be using the volume of a cone, otherwise, you have to do stuff like including an equation for the parabola shapes involved, the area defined by it...blah blah blah. 

volume of cone = 1.047 x (radius squared) x height, this is simplified, but close enough.

For the 'radius', take the largest diameter on the vessel and divide by 2, then square it (multiply it by itself). 
For the height, use distance from base to point of that largest diameter. 
The assumption I'm making is that the uncalculated volume above the 'largest diameter' point will wash out with what wasn't accounted for in the base.

Reactions: Like 1 | Thank You! 1


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## TimR (Nov 2, 2019)

TimR said:


> I don’t remember the calculus required but I'd think a good approximation would be using the volume of a cone, otherwise, you have to do stuff like including an equation for the parabola shapes involved, the area defined by it...blah blah blah.
> 
> volume of cone = 1.047 x (radius squared) x height, this is simplified, but close enough.
> 
> ...


If you want to get a bit closer, you could add a cone defined by the area from the opening to the largest diameter then subtract a cone defined by the base to an imaginary point below the base if you were to take the base to a “point”.

Reactions: Thank You! 1


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## ripjack13 (Nov 2, 2019)

Also using raw uncooked rice to find volume is an option. Sam Angelo has a video on this....

Reactions: Thank You! 1 | Agree 1


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## CWS (Nov 2, 2019)

You could fill the urn with rice. Dump the rice out into another vessel you can measure easily. just a thought

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## TimR (Nov 2, 2019)

Brent, the dilemma you have is coming up with an ideal size for the urn based on volumes of ashes expected. Just try plugging in some numbers by trial and error. If 200 cu in is the estimate, using the formula above, and maybe 9” tall at largest diameter, 
200 = 1.04 x radius squared x 9, so
200 = 9.36 x radius squared, so
200 / 9.36 = radius squared, so
21.4 = radius squared, so
4.6 = radius , so
9” = diameter 

So keep in mind these need to represent the interior dimensions , in this case an urn about 9.5” at widest outside diameter and assuming another 1/3 of height to opening, about 12” tall. 
Once you think you’ve got it, and you’ve made the urn, then you can check using the rice method @CWS and @ripjack13 described.

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## TimR (Nov 2, 2019)

Oh, once you have it all figured out on final size, add about 10% to err on big side.
Condolences to you and your wife’s family.

Reactions: Thank You! 1 | Agree 1


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## Lou Currier (Mar 26, 2021)

This was the urn I made for my dad. The base is approximately 5”, the height was approximately 18” at its highest point and the widest diameter was approximately 8”. I had 3 days to make it because he died suddenly so I just wung it. He was about 170 when he died and all the ashes fit with some room to spare so I got lucky  The top was just a slip on with no threads and was glued in place once the ashes were in there.

Reactions: EyeCandy! 2 | Sincere 3


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## Eric Rorabaugh (Mar 26, 2021)

Beautiful piece and tribute ❤


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## barry richardson (Mar 26, 2021)

That link Marc posted has a great soution, that's my kind of math lol

Reactions: Like 1


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