Question

A graduated cylinder contains 50 mL of water. You carefully place a rock into the cylinder, causing the water level to rise to 70 mL. If the mass of the rock is 100 grams, explain how to calculate the density of the rock in two to four sentences. Describe each step of the process and provide the final density value for full points. You may write your answer in complete sentences or as a numbered/bulleted list but you must explain all steps for full points.

Answer 1

To calculate the density of the rock, follow these steps:

1. Determine the volume of the rock: Since the water level rose from 50 mL to 70 mL after placing the rock in the graduated cylinder, the volume of the rock is the change in water level. This can be calculated as: \[ \text{Volume of the rock} = 70 , \text{mL} - 50 , \text{mL} = 20 , \text{mL} \]

2. Convert the volume to liters (if necessary): The volume in milliliters can also be expressed in liters, but since we are also using grams, we can continue with mL for density calculation in g/mL.

3. Use the density formula: Density is calculated using the formula: \[ \text{Density} = \frac{\text{Mass}}{\text{Volume}} \] Substitute the mass of the rock (100 grams) and the calculated volume (20 mL): \[ \text{Density} = \frac{100 , \text{g}}{20 , \text{mL}} = 5 , \text{g/mL} \]

4. Final result: The density of the rock is \(5 , \text{g/mL}\).