A gold prospector finds a solid rock that is composed solely of quartz and gold. The mass and volume of the rock are, respectively, 14.8 kg and 1.89 × 10-3 m3. The density of gold is 19 300 kg/m3, and the density of quartz is 2660 kg/m3. Find the mass of the gold in the rock.

Mass of gold in rock = 11.333 kg

Therefore rock is 76.58% gold

To find the mass of the gold in the rock, we first need to calculate the total mass of the rock using its density.

Density is defined as mass divided by volume, so we can rearrange the equation to solve for mass:

\[ \text{Mass} = \text{Density} \times \text{Volume} \]

The density of the rock is the sum of the densities of quartz and gold. Given that:

\[
\text{Density of gold} = 19,300 \, \text{kg/m}^3
\]
\[
\text{Density of quartz} = 2660 \, \text{kg/m}^3
\]

We can now calculate the total mass of the rock:

\[
\text{Mass} = (\text{Density of gold} + \text{Density of quartz}) \times \text{Volume}
\]

\[
\text{Mass} = (19,300 \, \text{kg/m}^3 + 2660 \, \text{kg/m}^3) \times 1.89 \times 10^{-3} \, \text{m}^3
\]

To find the mass of the gold in the rock, we need to determine the mass of the rock itself and subtract the mass of the quartz.

Step 1: Find the mass of the quartz in the rock.
The volume of the rock is given as 1.89 × 10-3 m3. The density of quartz is 2660 kg/m3. So, to find the mass of the quartz, we can multiply the volume by the density:

Mass of quartz = Volume × Density
= 1.89 × 10-3 m3 × 2660 kg/m3
= 5.0054 kg

Step 2: Find the mass of the gold in the rock.
The mass of the entire rock is given as 14.8 kg. We can now subtract the mass of the quartz to find the mass of the gold:

Mass of gold = Mass of rock - Mass of quartz
= 14.8 kg - 5.0054 kg
= 9.7946 kg

So, the mass of the gold in the rock is approximately 9.7946 kg.