Density Calculations Worksheet
Practice calculating density, mass, and volume using the fundamental density formula. Ensure you use the correct units and show your work where applicable.
Problem 1: Calculate Density
An object has a mass of 150 grams and a volume of 30 cm³. What is its density?
Show your work: D = M / V
Answer: ____________________ g/cm³
Problem 2: Calculate Mass
A substance has a known density of 2.5 g/mL. If you have a sample with a volume of 50 mL, what is its mass?
Show your work: M = D * V
Answer: ____________________ g
Problem 3: Calculate Volume
Gold has a density of approximately 19.3 g/cm³. If you have a gold nugget with a mass of 96.5 grams, what is its volume?
Show your work: V = M / D
Answer: ____________________ cm³
Problem 4: Word Problem – Rectangular Block
A rectangular block of aluminum measures 2 cm x 3 cm x 5 cm. If aluminum has a density of 2.7 g/cm³, what is the mass of the block?
Hint: First calculate the volume of the block.
Volume calculation: ____________________ cm³
Mass calculation: ____________________ g
Final Answer (Mass): ____________________ g
Problem 5: Conceptual Question
If you take a piece of wood and cut it exactly in half, what happens to the density of each half compared to the original piece?
Answer: _________________________________________________
Answer Key
1. Density: 150 g / 30 cm³ = 5 g/cm³
2. Mass: 2.5 g/mL * 50 mL = 125 g
3. Volume: 96.5 g / 19.3 g/cm³ = 5 cm³
4. Volume of block: 2 cm * 3 cm * 5 cm = 30 cm³.
Mass: 2.7 g/cm³ * 30 cm³ = 81 g
5. Conceptual: The density of each half remains the same as the original piece. Density is an intensive property, meaning it doesn’t depend on the amount of substance.
Understanding Density
Density is a fundamental physical property of matter. It’s defined as the mass of a substance per unit volume. Understanding density helps us predict whether an object will float or sink in a fluid, identify substances, and perform various scientific and engineering calculations.
Common units for density include:
- grams per cubic centimeter (g/cm³)
- grams per milliliter (g/mL) – Note: 1 cm³ = 1 mL
- kilograms per cubic meter (kg/m³)
Remember the density triangle to help you rearrange the formula: Cover the value you want to find, and the remaining two show you how to calculate it.
D = M / V | M = D × V | V = M / D