   SEARCH HOME Math Central Quandaries & Queries  I am digging a number of trenches 12" wide by 29" deep by 167ft long. In this trench there will be a 4.0 " tube I want to put 7" of top soil on top. So how many yards of gravel will I need and top soil will I need? Thank you Henry Hi Henry.

Is the 4 inches the diameter of the tube or the radius? I'll assume it is the diameter.

The top soil is well above the tube, so it is just a box-shape. The top soil needs to fill a space that measures 7" x 12" x 167 ft. Using our volume calculator, that is 3.65 cubic yards. Remember that this doesn't account for compacting of the top soil though - that will vary.

The gravel is the rest of the trench minus the volume of the tube. The rest of the trench is
(29-7)" x 12" x 167 ft, which you can multiply to get 44 088 in2 x ft. The volume of the tube is the area of the cross section (a circle with diameter 4" has an area of 4 x pi square inches) times the length of the tube: 4 x pi inches2 x 167 ft = 2099 in2 x ft. Subtracting these to get the volume of gravel, we get 44 088 - 2 099 = 41 989 in2 x ft. To convert that to cubic yards, we need to divide by 36 twice and divide by 3 once: 41 989 / 36 / 36 / 3 = 10.8 cubic yards.

So the volumes of gravel and topsoil are 10.8 and 3.65 cubic yards respectively, not accounting for compacting or "falling" of some topsoil in between the bits of gravel. You'd have to ask your contractor about that.

Stephen La Rocque.>     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.