Find the mass of \(1 \mathrm{~m}^{3}\) of gold in \(\mathrm{kg}\) when density of gold is \(19 \mathrm{~g} \mathrm{~cm}^{-3}\).

Understanding the relationship between mass and volume is fundamental in physics and applied sciences. Mass is a measure of the amount of matter in an object, typically expressed in units such as grams (g) or kilograms (kg). Volume, on the other hand, measures the amount of space an object occupies and is often expressed in cubic centimeters (cm³) or cubic meters (m³). The exercise involves finding the mass of gold given its volume.

When solving problems like these, the crucial step is to ensure that the units of mass and volume are compatible with the units in the density value provided. In this case, the density of gold is provided in grams per cubic centimeter, so we initially need to express the volume of gold in cubic centimeters even though it was provided in cubic meters. By doing this, we ensure that we can directly multiply the density by the volume to find the mass.

Unit conversion is a staple in solving physics and chemistry problems. It's about changing from one unit of measurement to another without changing the quantity. In our exercise, we encountered two key conversions: from cubic meters to cubic centimeters for volume, and from grams to kilograms for mass.

1 cubic meter equals 1,000,000 cubic centimeters, and 1 kilogram equals 1,000 grams. Understanding and applying correct conversion factors is critical. Remember that units may need to be converted so that they align with the standard units used for specific physical quantities. In this case, converting the calculated mass from grams to kilograms made it consistent with common usage, where mass is often expressed in kilograms.

Gold is a chemical element with unique physical properties that make it highly valuable and widely utilized in various industries including jewelry, electronics, and investment. One of its key physical properties is density, which is given as 19 g/cm³ in this exercise.

Density is a measure of how much mass is contained within a unit volume. For gold, a high density means that even a small amount of this metal has a relatively large mass. Knowing the density of gold, coupled with the volume, allows the calculation of the mass of gold for any given volume. This property is crucial for various applications; for instance, it allows jewelers to estimate the weight of gold items and investors to assess the purity of gold bullion.