This section is from the book "Commercial Gardening Vol3", by John Weathers (the Editor). Also available from Amazon: Commercial Gardening, A Practical & Scientific Treatise For Market Gardeners.
It is a little more complicated to gauge the cubic contents of these accurately, because they are not cylindrical, square, or rectangular bodies, but truncated cones - broader at the top than at the bottom. The volume of any flower pot may be found by the following rule: To the areas of the two ends add the square root of their 'product, multiply the sum by the height of the pot, and one-third of the product will be the volume. Taking a 5-in. or 48-sized pot, which is probably the most largely used size in the trade, the dimensions are: Top width 5 in., bottom width 3 in., depth 4$ in. To find volume proceed as follows: Area of top 5 x 5 x .7854 = 196 sq. in.; area of bottom 3 x 3 x .7854 = 7 sq. in. Product of areas = 19.6 x 7 = 1372. Square root of 137 = 117. Add square root to areas of top and bottom, 196 + 7 + 11.'7 = 38.
Multiply by depth, 4 1/2 = 38 x 4 1/2 = 171. Divide by 3 = 171/3 = 57 cub. in., the required contents of a 5-in. pot - equivalent to 164 pt. of water.
In the same way it may be found that the cubic contents of a 6-in. or 33-sized pot is about 108 cub. in. - equivalent to 3.11 pt. of water.
With the help of this rule it is easy to estimate the quantities of soil or compost required for any particular crop. For instance, if 10,000 Zonal Pelargoniums are to be placed in 5-in. pots (48's), this will mean 570,000 cub. in. of soil = 329 cub. ft. = 12 cub. yd. = about 12 tons.