Given 0.65 cubic feet of a soil sample weighing 36.2 pounds with a moisture content of 15%, what is the dry density of the soil?

To find the dry density of the soil, we first need to understand the relationship between the wet weight of the soil, its moisture content, and its dry density.

The formula for calculating dry density is given by:

Dry Density = Weight of Dry Soil / Volume of Soil

In this case, the total weight of the soil sample is 36.2 pounds, and the moisture content is 15%. To determine the weight of the dry soil, we can use the formula:

Weight of Dry Soil = Wet Weight / (1 + Moisture Content)

Here, the moisture content is expressed as a decimal in the calculations, so 15% becomes 0.15. Now we can calculate the weight of dry soil:

Weight of Dry Soil = 36.2 pounds / (1 + 0.15)

= 36.2 pounds / 1.15

≈ 31.52 pounds

Now that we have the weight of the dry soil, we can calculate the dry density by dividing the weight of the dry soil by the volume, which is 0.65 cubic feet:

Dry Density = 31.52 pounds / 0.65 cubic feet

≈ 48.4 pounds/c