Density Practice Problems- Worksheet with Solutions
What You Need to Know About Density Before You Start
Density is how much mass fits into a given volume. That's it. The formula is d = m / v — mass divided by volume. Most students either forget the formula or mix up which unit goes where.
This worksheet gives you 12 practice problems with full solutions. Work through them. If you get stuck, the answer shows exactly how to set it up.
The Density Formula
d = m ÷ v
Where:
- d = density (usually g/cm³ or g/mL)
- m = mass (usually grams)
- v = volume (usually cm³ or mL)
You can rearrange it depending on what you're solving for:
- Find density: d = m ÷ v
- Find mass: m = d × v
- Find volume: v = m ÷ d
How to Solve Any Density Problem
Step 1: Identify what you're given — mass, volume, or density.
Step 2: Identify what you need to find.
Step 3: Pick the right formula.
Step 4: Plug in the numbers. Always include units.
Step 5: Calculate. Check your units — if grams and cm³ cancel out, you're probably right.
Density Practice Problems
Problems 1–4: Find the Density
| Problem | Question | Answer |
|---|---|---|
| 1 | A block has a mass of 200 g and a volume of 50 cm³. What is its density? | 4 g/cm³ d = 200 g ÷ 50 cm³ = 4 g/cm³ |
| 2 | A liquid sample has a mass of 75 g and a volume of 100 mL. What is its density? | 0.75 g/mL d = 75 g ÷ 100 mL = 0.75 g/mL |
| 3 | A metal sphere has a mass of 450 g and a volume of 60 cm³. Calculate the density. | 7.5 g/cm³ d = 450 g ÷ 60 cm³ = 7.5 g/cm³ |
| 4 | An irregular object has a mass of 32 g. When dropped into water, it displaces 8 mL. What is the density? | 4 g/mL d = 32 g ÷ 8 mL = 4 g/mL (volume = 8 cm³) |
Problems 5–8: Find the Mass
| Problem | Question | Answer |
|---|---|---|
| 5 | A cube of aluminum has a density of 2.7 g/cm³ and a volume of 20 cm³. What is its mass? | 54 g m = 2.7 g/cm³ × 20 cm³ = 54 g |
| 6 | A block of wood with density 0.6 g/cm³ has a volume of 150 cm³. What is its mass? | 90 g m = 0.6 g/cm³ × 150 cm³ = 90 g |
| 7 | Gold has a density of 19.3 g/cm³. What is the mass of a gold nugget with volume 2.5 cm³? | 48.25 g m = 19.3 g/cm³ × 2.5 cm³ = 48.25 g |
| 8 | A balloon filled with helium has a density of 0.18 g/L and a volume of 500 L. What is the mass of the helium? | 90 g m = 0.18 g/L × 500 L = 90 g |
Problems 9–12: Find the Volume
| Problem | Question | Answer |
|---|---|---|
| 9 | A rock has a mass of 250 g and a density of 5 g/cm³. What is its volume? | 50 cm³ v = 250 g ÷ 5 g/cm³ = 50 cm³ |
| 10 | A piece of copper has a mass of 890 g and a density of 8.9 g/cm³. What is its volume? | 100 cm³ v = 890 g ÷ 8.9 g/cm³ = 100 cm³ |
| 11 | A mystery liquid has a mass of 180 g and a density of 0.9 g/mL. What volume does it occupy? | 200 mL v = 180 g ÷ 0.9 g/mL = 200 mL |
| 12 | An ice cube has a mass of 36 g and a density of 0.92 g/cm³. What is its volume? | ≈39.1 cm³ v = 36 g ÷ 0.92 g/cm³ = 39.13 cm³ |
Quick Reference: Density of Common Substances
| Substance | Density (g/cm³) |
|---|---|
| Water | 1.0 |
| Ice | 0.92 |
| Aluminum | 2.7 |
| Iron / Steel | 7.8 |
| Copper | 8.9 |
| Lead | 11.3 |
| Gold | 19.3 |
| Oak wood (avg) | 0.6–0.9 |
Where Students Mess Up
Unit mismatches: If mass is in kg and volume is in cm³, convert first. 1 kg = 1000 g. 1 mL = 1 cm³.
Forgetting to convert volume: If a problem gives dimensions (cm × cm × cm), multiply them to get cm³. Don't just use one measurement.
Flipping the formula: Students often write v = d/m instead of v = m/d. Draw a triangle if you need to — mass on top, volume on bottom, density over the line.
Water displacement confusion: When an object is submerged, the water level rise equals the object's volume. That's volume in mL or cm³ — they're the same.
That's the Worksheet
Work through all 12 problems until you can solve each one without checking the answers first. If a problem gives you trouble, figure out which step is the problem — identifying given info, picking the formula, or the arithmetic.
The math here is basic division and multiplication. The hard part is knowing what numbers go where.