1. Let's state the problem: We want to understand the relationship between mass, weight, and density. 2. Definitions: - Mass ($m$) is the amount of matter in an object, measured in kilograms (kg). - Weight ($W$) is the force exerted by gravity on that mass, measured in newtons (N). - Density ($\rho$) is mass per unit volume, measured in kilograms per cubic meter (kg/m$^3$). 3. The formulas: - Weight is related to mass by the formula $$W = m \times g$$ where $g$ is the acceleration due to gravity (approximately 9.8 m/s$^2$ on Earth). - Density is defined as $$\rho = \frac{m}{V}$$ where $V$ is the volume. 4. Combining these, if you know the density and volume, you can find mass: $$m = \rho \times V$$ 5. Then weight can be found by substituting mass into the weight formula: $$W = (\rho \times V) \times g$$ 6. Summary: Weight depends on mass and gravity, mass depends on density and volume, so weight can be expressed as $$W = \rho \times V \times g$$. This shows how mass, weight, and density are related through volume and gravity.