Math CentralQuandaries & Queries


Question from Debbie:

A trench 100metres long 1ft wide*18inches deep with a 4inch pipe laid.
How much stone will be needed to fill the trench?
How much weight in stone would I need to fill it?

The amount needed is the volume of the trench (length times width times depth) minus the volume of the pipe (pi times the square of the radius times the length). The radius of a circle is half of its diameter.

Before doing any computations, it is necessary to convert everything to the same units -- right now there are feet, inches and metres. One foot = 12 inches = 0.254 metres. As a practical matter, it might be best to convert to the same units in which the stone is ordered. This is, if the stone is ordered in cubic feet, then convert everything to feet before calculating, etc.

Also, is the diameter of the pipe measured from outside edge to outside edge? If it is from inside edge to inside edge, then the volume of material used to make the pipe is missing from the calculation.

Victoria West


You sent a second question asking the weight of the stone. To determine that you need the density of the particular stone you are using. You will probably have to ask the stone supplier for the density.


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