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Guy Bratt
Here's an excerpt from Mike Stafford's article in More Woodturning Magazine June 2015. Just the math.

Time for Some Math

As I conducted my research for this project I found information from a number of other turners who generally agreed that one should plan on having an internal volume sufficient to hold at least one cubic inch per pound of body weight before cremation. Taffy was a not-so-svelte little girl at somewhere near 20 pounds. So I would need a hollowed out area in my urn of at least 20 cubic inches. One source I found said I could use rice to determine the required space by measuring the equivalent volume in an ordinary measuring cup containing the correct amount of dry rice which is both retrievable and reusable. But the question remained: How much rice?

I found a web site which helped me determine this answer:

The conversion table on this site provides the information necessary to determine the volume 20 cubic inches (or virtually any number of cubic inches for that matter) will occupy by use of an ordinary measuring cup. The table shows that 20 cubic inches of cremains will occupy 11.1 ounces in a liquid measuring cup. Now with rice and a plastic bag I can visualize the size of the internal volume required for the urn. I measured 12 ounces of rice in a measuring cup and put it in a plastic bag. I then laid the plastic bag of rice roughly formed into the shape I envisioned for the interior of my urn on my spalted hackberry blank. I positioned the bag of rice so that it was in the area where the body cavity of my urn would be located. It was obvious by doing this that my piece of wood was going to be large enough to accommodate the volume I wanted to enclose (see Figure 3).

FIGURE 3

And Some More Math

For those of you who are more mathematically inclined and wish to more accurately determine the volume of the hollow form I suggest you think of the interior shape as a truncated cone; i.e., a cone with the pointed end cut off. By determining the diameter/radii at the top and bottom and height of the hollow area inside the urn there is a formula that can be used to accurately calculate the volume.

Volume= â…“ π (r12 + r1r2 + r22) H

Or more simply just go to this link and plug in the height, radius of the major diameter, radius of the minor diameter and hit calculate to let their computer do the work for you.

keisan.casio.com/has10/SpecExec.cgi?id=system/2006/1223372110

Once this volume is known, the trick with the rice can be used to visualize the internal volume needed for the cremains.