Density Worksheet - New York Science Teacher - Free Printable

Let’s solve this Density Worksheet step by step.

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## ✔ STEP 1: Calculate Density for Samples 1–5

The formula for density is:

> Density (d) = Mass (m) / Volume (v)
> Units: g/cm³

We’ll calculate the density for each sample using the given mass and volume.

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Sample 1:

- Mass = 15 g
- Volume = 2 cm³
- Density = 15 / 2 = 7.5 g/cm³

Sample 2:

- Mass = 60 g
- Volume = 8 cm³
- Density = 60 / 8 = 7.5 g/cm³

Sample 3:

- Mass = 120 g
- Volume = 16 cm³
- Density = 120 / 16 = 7.5 g/cm³

Sample 4:

- Mass = 480 g
- Volume = 64 cm³
- Density = 480 / 64 = 7.5 g/cm³

Sample 5:

- Mass = 750 g
- Volume = 100 cm³
- Density = 750 / 100 = 7.5 g/cm³

✔ All samples have the same density: 7.5 g/cm³

This makes sense — they are all samples of the *same mineral*: galena. Density is an *intensive property* — it doesn’t change with sample size.

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## ✔ STEP 2: Fill in the Data Table

| Sample | Size | Mass | Volume | Density (d=m/v) |
|--------|--------|-------|--------|------------------|
| 1 | small | 15 g | 2 cm³ | 7.5 g/cm³ |
| 2 | | 60 g | 8 cm³ | 7.5 g/cm³ |
| 3 | | 120 g | 16 cm³ | 7.5 g/cm³ |
| 4 | | 480 g | 64 cm³ | 7.5 g/cm³ |
| 5 | large | 750 g | 100 cm³| 7.5 g/cm³ |

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## ✔ STEP 3: Answer the Questions

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1. Use the completed graph to determine how much mass a sample of galena would have if its volume was 75 cm³.

Since density is constant (7.5 g/cm³), we can use:

> Mass = Density × Volume

Mass = 7.5 g/cm³ × 75 cm³ = 562.5 g

*(Note: If you plotted the graph, you’d see a straight line through the origin — so at 75 cm³ on x-axis, y-axis (mass) would be 562.5 g)*

✔ Answer: 562.5 grams

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2. Use the completed graph to determine how much volume a sample of galena would have if its mass was 300 g.

Use:

> Volume = Mass / Density

Volume = 300 g / 7.5 g/cm³ = 40 cm³

✔ Answer: 40 cm³

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3. Describe the relationship between mass and volume shown by the graph.

The graph will show a straight line passing through the origin (0,0), meaning mass is directly proportional to volume.

This is because density is constant — as volume increases, mass increases at the same rate.

✔ Answer: Mass and volume are directly proportional — as volume increases, mass increases proportionally. The graph is a straight line through the origin.

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4. How does the density of Sample 2 compare to that of Sample 4?

Both have density = 7.5 g/cm³

✔ Answer: They are equal. Density does not depend on sample size.

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5. How did the density of the largest sample (5) compare to the smallest sample (1)?

Sample 5: 750 g / 100 cm³ = 7.5 g/cm³
Sample 1: 15 g / 2 cm³ = 7.5 g/cm³

✔ Answer: They are identical. Density is an intensive property and does not change with sample size.

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6. What is the effect of sample size on the density of a material?

None. Density is an intensive property — it depends only on the type of material, not on how much you have.

✔ Answer: Sample size has no effect on density. Density remains constant regardless of sample size for a pure substance.

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7. Describe the trick you were taught on how to change around the density formula to solve for different parts of it.

This refers to rearranging the formula d = m/v using algebra or the “density triangle”.

#### 📐 Density Triangle Method:
Draw a triangle and divide it into 3 parts:

```
M
---
D | V
```

Cover the variable you want to solve for:

- Cover M → you get D × V
- Cover D → you get M ÷ V
- Cover V → you get M ÷ D

#### 🔁 Algebraic Rearrangement:
From d = m/v, multiply both sides by v → m = d × v

Divide both sides by d → v = m/d

✔ Answer: You can rearrange the formula d = m/v to solve for any variable:
- To find mass: m = d × v
- To find volume: v = m ÷ d
- You can also use the “density triangle” — cover the variable you want to find, and the remaining two show the operation.

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## ✔ FINAL SUMMARY

- All samples of galena have density = 7.5 g/cm³
- Mass and volume are directly proportional
- Density is independent of sample size
- You can rearrange d = m/v to solve for mass or volume

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📌 Bonus Tip: This worksheet teaches a key concept in science — density is a characteristic property of a substance. No matter how big or small the sample, if it’s pure galena, its density will always be ~7.5 g/cm³!

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✔ All questions answered! Let me know if you’d like help plotting the graph too.