Question

A sandstone sample with 100 % quartz has a porosity of 30 %. The sample is dry and the density of quartz is 2.65 g/cc. The bulk density of the sandstone sample is ............ g/cc. (Round off to one decimal place)

Hint:

When calculating bulk density for a porous sample, multiply the density of the material by the fraction of solid material (1 - porosity).

Answer 1

Correct Answer: 1.9

Given: 
- Porosity (\(\phi\)) = 30% = 0.30 
- Density of quartz (\(\rho_q\)) = 2.65 g/cc 
- The sample is 100% quartz, so the non-porous fraction is 70% (since 30% is porosity). 
Step 1: The bulk density \(\rho_b\) can be calculated using the formula: 
\[ \rho_b = (1 - \phi) \times \rho_q \] 

Step 2: Substitute the known values into the formula: 
\[ \rho_b = (1 - 0.30) \times 2.65 \] 

Step 3: Simplify the calculation: 
\[ \rho_b = 0.70 \times 2.65 = 1.855 \, \text{g/cc} \] 

Step 4: Round to one decimal place: 
\[ \rho_b = 1.9 \, \text{g/cc} \] 
Thus, the bulk density of the sandstone sample is **1.9 g/cc**.
\[ \boxed{1.9 \, \text{g/cc}} \]