Math CentralQuandaries & Queries


Question from Zach:


I'm looking for amount of stone dust needed for thirteen holes with a 3ft depth and 12in diameter with a 4x4 post. I would need the measurement in KG.


Hi Zach,

A top down view of one of the holes with the post inside it is a circle of radius 6 inched with a square post of side length 3.75 inches (4 inch posts are actually 3.75 inches on each side). Thus the area of the stone dust on the top of the hole is

\[\pi \; r^2 - 3.75^2 = \pi \; 6^2 - 3.75^2 = 99.03 \mbox{ square inches.}\]

The depth of each hole is $3 \times 12 = 36$ inches so the volume of stone dust in each hole is

\[36 \times 99.03= 3565.25 \mbox{ cubic inches.}\]

If you want this in other units you can ask Google. In particular typing what is 3565.25 cubic inches in cubic meters in the Google search window gives an answer of 0.058 cubic meters.

You have 13 holes for a total stone dust volume of $13 \times 3565.25 = 46,348.30$ cubic inches.

As for the weight I need to know the density of stone dust. I did a search of the web an found some information, in particular Anshuman Stone Crusher in India which states that the density of Stone Aggregate Crusher Dust is 1880 kilograms per cubic meter. You might find a better reference for the particular stone dust you are using.


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