1. **Problem statement:** Given a soil sample with: - Initial mass (wet mass) $M = 301.4$ g - Dry mass $M_d = 258.0$ g - Total volume $V = 161.4$ cm$^3$ - Relative density (specific gravity) $G = 2.66$ Find: - Mass of water - Volume of water - Volume of solids - Density - Dry density - Water content - Void ratio - Porosity 2. **Formulas and important rules:** - Mass of water $M_w = M - M_d$ - Volume of solids $V_s = \frac{M_d}{G \times \rho_w}$ where $\rho_w = 1$ g/cm$^3$ (density of water) - Volume of water $V_w = V - V_s$ - Density $\rho = \frac{M}{V}$ - Dry density $\rho_d = \frac{M_d}{V}$ - Water content $w = \frac{M_w}{M_d} \times 100\%$ - Void ratio $e = \frac{V_w}{V_s}$ - Porosity $n = \frac{V_w}{V} \times 100\%$ 3. **Calculations:** - Mass of water: $$M_w = 301.4 - 258.0 = 43.4\text{ g}$$ - Volume of solids: $$V_s = \frac{258.0}{2.66 \times 1} = \frac{258.0}{2.66} = 97.0\text{ cm}^3$$ - Volume of water: $$V_w = 161.4 - 97.0 = 64.4\text{ cm}^3$$ - Density: $$\rho = \frac{301.4}{161.4} = 1.9\text{ g/cm}^3$$ - Dry density: $$\rho_d = \frac{258.0}{161.4} = 1.6\text{ g/cm}^3$$ - Water content: $$w = \frac{43.4}{258.0} \times 100 = 16.8\%$$ - Void ratio: $$e = \frac{64.4}{97.0} = 0.7$$ - Porosity: $$n = \frac{64.4}{161.4} \times 100 = 39.9\%$$ 4. **Summary:** - Mass of water = 43.4 g - Volume of water = 64.4 cm$^3$ - Volume of solids = 97.0 cm$^3$ - Density = 1.9 g/cm$^3$ - Dry density = 1.6 g/cm$^3$ - Water content = 16.8 % - Void ratio = 0.7 - Porosity = 39.9 %