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, it's essential to understand the relationship between the weight of the soil, its moisture content, and its volume. The moisture content indicates how much water is present in the soil, expressed as a percentage of the weight of the dry soil.

First, let's calculate the dry weight of the soil. The wet weight given is 36.2 pounds, and the moisture content of 15% means that 15% of the dry weight is made up of water. We can represent the dry weight as ( D ):

[

\text{Wet Weight} = D + 0.15D = 1.15D

]

Setting the equation equal to the wet weight:

[

1.15D = 36.2

]

Now, solve for ( D ):

[

D = \frac{36.2}{1.15} \approx 31.48 \text{ pounds}

]

Next, we need to find the dry density, which is the dry weight per unit volume of soil. The volume of the soil sample given is 0.65 cubic feet.

To find the dry density, use the formula:

[

\text{Dry Density} =