## Thursday, December 4, 2014

### How much does a millstone weigh?

Not far from the college where I teach is an old millstone laying decoratively on the ground.

I've been doing some research on millstones lately so I was wondering how much a typical millstone like this would weigh.  Measuring it gives the following dimensions:

Diameter = 53 in
Thickness = 8 in
Hole = 13 in square

This millstone happens to be made of Shawangunk conglomerate which is composed almost entirely of quartz.  All geologists know the density of quartz which is 2.7 g/cm3.  I want to keep everything in more familiar units so that corresponds to about 0.1 lb/in3.

The volume (V) of the millstone would be:

V = π (d/2)2 t

where d is the diameter of the millstone and t is the thickness.

V = 3.14 (53 in / 2)2 (8 in)
V =  17,641 in3

We have to subtract out the volume of the square hole in the middle (13 in * 13 in * 8 in = 1,352 in3)

V = 17,641 in3 - 1,352 in3
V = 16,289 in3

Now we can multiply this by the density of quartz to get the weight of the millstone.

Weight = 16,289 in3 * 0.1 lb/in3 = 1,629 lb

Over 3/4 ton!  Imagine moving this many miles, over rough terrain, with man power, a wagon, and maybe a mule or two.