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Granite is an important concept when analyzing rocks and geological specimens. It is a common type of intrusive igneous rock. Its structure is compositionally diverse, typically consisting of quartz, feldspar, and mica. This rock forms from the slow crystallization of magma beneath the Earth's surface. Because of its durability and aesthetic appeal, granite is often used in construction and as a decorative stone.

In the context of the problem exercise, granite is characterized by its density, which is crucial for calculations. The density of granite, given as \(\rho_{\text{granite}} = 2650 \, \text{kg/m}^3\), helps in determining the mass of granite within a composite rock containing gold and granite. Density is a physical property defined as mass per unit volume and is used in various calculations to determine the composition of rocks.

• Density - The mass of a substance per unit volume, typically expressed in \(\text{kg/m}^3\).
• Granite Density - For granite, this is \(2650 \, \text{kg/m}^3\), which is useful for understanding its contribution to the total mass of a rock.

Granite's density allows us to model and calculate its specific mass in composite formations, like those found by prospectors, based on the given total mass and volume of the specimen.

Mass percentage is a useful measurement in determining the composition of a mixture or sample, especially in geology when dealing with rocks. It refers to the percentage of the total mass that a specific component contributes. This helps in understanding how much of a sample consists of a particular substance.

To calculate the mass percentage of gold in the rock, you need to know the mass of gold present and the total mass of the rock. The formula used is:\[\text{Mass percentage of gold} = \left( \frac{m_{au}}{m_{\text{total}}} \right) \times 100\%\]where \(m_{au}\) is the mass of the gold and \(m_{\text{total}}\) is the total mass of the rock.

• The mass of gold is found by subtracting the mass of granite from the total mass: \(m_{au} = m_{\text{total}} - m_{g}\).
• The total mass of the rock is given as \(3.81 \, \text{kg}\).

This approach offers a clear picture of how the mass of different components like gold contribute to the total mass of a geological specimen.

Volume percentage is a vital concept for understanding how much space a certain component occupies in relation to the total volume. This is especially important when working with rocks to determine how much of a sample is comprised of a specific material.

In the exercise, the volume percentage of gold in the rock is needed. To find it, first calculate the volume of gold using its density, which is \(19300 \, \text{kg/m}^3\), and the mass of the gold obtained previously. The relationship is given by:\[V_{au} = \frac{m_{au}}{\rho_{\text{gold}}}\]where \(V_{au}\) is the volume of gold and \(\rho_{\text{gold}}\) is the density of gold. Then, use the total volume of the rock to find the volume percentage:\[\text{Volume percentage of gold} = \left( \frac{V_{au}}{V_{\text{total}}} \right) \times 100\%\]where \(V_{\text{total}}\) is the total volume of the rock.

• Volume of gold - Calculated by dividing the mass of gold by its density.
• Total volume - In the problem, the given total volume is \(3.55 \times 10^{-4} \, \text{m}^3\).

Using volume percentages provides insights into the spatial composition of geological mixtures, offering a better understanding of the proportions of materials like gold in rock formations.