Density Worksheet - New York Science Teacher - Free Printable

Let’s solve this step by step, following the Density Worksheet instructions.

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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 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’re all samples of the same mineral: galena.

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## ✔ STEP 2: Fill in the “Density” column in the 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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Question 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, it should be a straight line through the origin with slope = 7.5. At volume = 75 cm³, mass = 562.5 g.)*

✔ Answer: 562.5 grams

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

The graph shows a straight line passing through the origin, meaning mass is directly proportional to volume.

This indicates that as volume increases, mass increases at a constant rate — which is characteristic of a material with constant density.

✔ Answer: Mass and volume are directly proportional. The graph is a straight line through the origin, indicating constant density.

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

As calculated earlier:

- Sample 2 density = 7.5 g/cm³
- Sample 4 density = 7.5 g/cm³

✔ Answer: They are equal. Both have a density of 7.5 g/cm³.

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

Sample 5 (largest): 7.5 g/cm³
Sample 1 (smallest): 7.5 g/cm³

✔ Answer: They are identical. Density does not change with sample size for the same material.

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

Density is an intensive property — it does not depend on the amount (size) of the sample. Whether you have a tiny piece or a large block of the same pure substance, the density remains the same.

✔ Answer: Sample size has no effect on density. Density is constant for a given material regardless of sample size.

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Question 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 density formula using algebra or the “triangle method”.

The basic formula:
> d = m / v

To solve for mass:
> m = d × v

To solve for volume:
> v = m / d

Trick (Triangle Method):

Draw a triangle and divide it into 3 sections:

```
m
-----
d | v
```

Cover the variable you want to solve for:

- Cover m → you see d × v → so m = d × v
- Cover d → you see m / v → so d = m / v
- Cover v → you see m / d → so v = m / d

✔ Answer: The “density triangle” trick — cover the variable you want to solve for, and the remaining variables show you how to calculate it. For example, cover ‘m’ to get m = d × v; cover ‘v’ to get v = m / d.

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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 any variable using the triangle method or algebra

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