You solve density problems by using the formula: Density = Mass / Volume (D = M/V). Here's a breakdown of the process:
1. Understand the Density Formula
Density is a measure of how much mass is contained in a given volume. The formula expresses this relationship:
- Density (D): Usually expressed in units like grams per cubic centimeter (g/cm³) or kilograms per cubic meter (kg/m³).
- Mass (M): The amount of substance, typically measured in grams (g) or kilograms (kg).
- Volume (V): The amount of space the substance occupies, usually measured in cubic centimeters (cm³) or cubic meters (m³).
2. Identify Knowns and Unknowns
Read the problem carefully and determine:
- What are you trying to find? (Is it density, mass, or volume?)
- What information are you given? (Mass and volume? Density and volume? etc.)
3. Apply the Density Formula
Depending on what you're solving for, rearrange the formula:
- To find Density (D): D = M / V
- To find Mass (M): M = D * V
- To find Volume (V): V = M / D
4. Use Consistent Units
This is crucial! Make sure your units are compatible before performing calculations. If they are not, you'll need to convert them. For example:
- If mass is in kilograms (kg) and volume is in cubic centimeters (cm³), you might want to convert kilograms to grams (1 kg = 1000 g) or cubic centimeters to cubic meters (1 m³ = 1,000,000 cm³) to match the desired density unit.
5. Perform the Calculation
Plug the known values (with their correct units) into the rearranged formula and calculate the answer.
6. Report the Answer with Correct Units
The final answer must include the appropriate units. If you calculated density and used grams for mass and cubic centimeters for volume, the density would be expressed in g/cm³.
Example Problem
A rock has a mass of 150 grams and a volume of 50 cm³. What is its density?
- Identify:
- Unknown: Density (D)
- Known: Mass (M = 150 g), Volume (V = 50 cm³)
- Formula: D = M / V
- Calculation: D = 150 g / 50 cm³ = 3 g/cm³
- Answer: The density of the rock is 3 g/cm³.
Tips for Success
- Read carefully: Understand what the problem is asking.
- Write down knowns and unknowns: Organize the information.
- Pay attention to units: Unit conversion is a common source of errors.
- Show your work: This helps in identifying and correcting mistakes.
- Practice: The more you practice, the easier it becomes.
