Practice: Density Problems

Problem 1: The Golden Cube

A cube of gold has a side length of 2 cm. The density of gold is $19.3 \text{ g/cm}^3$. What is the mass of the cube?

Solution:

1. Find Volume: $V = side \times side \times side = 2 \times 2 \times 2 = 8 \text{ cm}^3$.
2. Use Formula: $\text{Mass} = \text{Density} \times \text{Volume}$.
3. Calculate: $Mass = 19.3 \times 8 = 154.4 \text{ g}$.

Problem 2: The Mystery Liquid

You have a beaker weighing 50g. You add 100 mL of a mystery liquid. The combined weight is 130g. What is the density of the liquid?

Solution:

1. Find Liquid Mass: $130\text{g (Total)} - 50\text{g (Beaker)} = 80\text{g}$.
2. Liquid Volume: 100 mL (which is $100 \text{ cm}^3$).
3. Calculate: $\text{Density} = 80 / 100 = 0.8 \text{ g/cm}^3$.

• Inference: This is likely alcohol or oil (less dense than water).

Problem 3: Relative Density

The relative density of Silver is 10.8. The density of water is $1000 \text{ kg/m}^3$. What is the density of Silver in SI units?

Solution:

• $\text{Relative Density} = \frac{\text{Density of Substance}}{\text{Density of Water}}$.
• $10.8 = \frac{\text{Density of Silver}}{1000}$.
• $\text{Density of Silver} = 10.8 \times 1000 = 10,800 \text{ kg/m}^3$.