SOLUTION: Density calculations worksheet 1 - Studypool - Free Printable

The worksheet you've uploaded is a Density Calculations Worksheet for Grade 9 science, focusing on the concept of density using the formula:

$$
\text{Density} = \frac{\text{Mass}}{\text{Volume}} \quad \text{or} \quad d = \frac{M}{V}
$$

Let’s go through each section and verify the solutions, then explain how to solve them correctly. There are some errors in the provided answers that need correction.

---

🔹 Section 1: Find the unknown quantity

#### a)
Given:
- $ d = 3 \, \text{g/mL} $
- $ V = 100 \, \text{mL} $
- $ M = ? $

Correct Solution:
$$
M = d \times V = 3 \, \text{g/mL} \times 100 \, \text{mL} = 300 \, \text{g}
$$
✔ Correct

---

#### b)
Given:
- $ V = 950 \, \text{mL} $
- $ M = 95 \, \text{g} $
- $ d = ? $

Incorrect Calculation in Worksheet:
It says:
$$
d = \frac{M}{V} = \frac{95}{950} = 0.1 \quad \Rightarrow \quad d = 0.1 \, \text{g/mL}
$$
This is correct — but let's double-check:
$$
\frac{95}{950} = 0.1 \, \text{g/mL} \quad \text{✓ Correct}
$$

✔ Correct

---

#### c)
Given:
- $ d = 0.5 \, \text{g/cm}^3 $
- $ M = 20 \, \text{g} $
- $ V = ? $

Solution:
$$
V = \frac{M}{d} = \frac{20}{0.5} = 40 \, \text{cm}^3
$$
✔ Correct

---

🔹 Section 2: Convert first to g or mL

#### a)
Given:
- $ d = 24 \, \text{g/mL} $
- $ V = 1.2 \, \text{L} = 1200 \, \text{mL} $ (since $ 1 \, \text{L} = 1000 \, \text{mL} $)
- $ M = ? $

$$
M = d \times V = 24 \times 1200 = 28,800 \, \text{g}
$$
✔ Correct

---

#### b)
Given:
- $ V = 100 \, \text{mL} $
- $ M = 1.5 \, \text{kg} = 1500 \, \text{g} $ (since $ 1 \, \text{kg} = 1000 \, \text{g} $)
- $ d = ? $

$$
d = \frac{M}{V} = \frac{1500}{100} = 15 \, \text{g/mL}
$$
✔ Correct

---

#### c)
Given:
- $ V = 0.52 \, \text{L} = 520 \, \text{mL} $
- $ M = 500 \, \text{mg} = 0.5 \, \text{g} $ (since $ 1000 \, \text{mg} = 1 \, \text{g} $)
- $ d = ? $

$$
d = \frac{M}{V} = \frac{0.5}{520} = 0.0009615... \approx 0.00096 \, \text{g/mL}
$$
✔ Correct (rounded appropriately)

---

🔹 WORD PROBLEMS

#### 1. A block of aluminum occupies a volume of 15.0 mL and weighs 40.5 g. What is its density?

Given:
- $ V = 15.0 \, \text{mL} $
- $ M = 40.5 \, \text{g} $

$$
d = \frac{M}{V} = \frac{40.5}{15.0} = 2.7 \, \text{g/mL}
$$

✔ Correct

> Note: This matches the known density of aluminum (~2.7 g/mL), so it makes sense.

---

✔ Summary of All Answers

| Problem | Answer |
|--------|--------|
| 1a) Mass | 300 g |
| 1b) Density | 0.1 g/mL |
| 1c) Volume | 40 cm³ |
| 2a) Mass | 28,800 g |
| 2b) Density | 15 g/mL |
| 2c) Density | 0.00096 g/mL |
| Word Problem | 2.7 g/mL |

All calculations shown in the worksheet are correct!

---

📝 Explanation of Key Concepts

- Density Formula:
$$
d = \frac{M}{V}
$$
You can rearrange this to find:
- $ M = d \times V $
- $ V = \frac{M}{d} $

- Units Matter!
- For liquids: use g/mL
- For solids: use g/cm³
- But note: $ 1 \, \text{mL} = 1 \, \text{cm}^3 $, so they are equivalent.

- Unit Conversions:
- $ 1 \, \text{L} = 1000 \, \text{mL} $
- $ 1 \, \text{kg} = 1000 \, \text{g} $
- $ 1 \, \text{g} = 1000 \, \text{mg} $

Always convert to consistent units before plugging into formulas.

---

✔ Final Thoughts

The worksheet has been completed correctly with accurate calculations and proper unit conversions. The student demonstrated good understanding of:
- Density formula
- Unit conversions
- Rearranging equations

Well done! If you're reviewing this, make sure to practice similar problems involving different units and real-world applications (like identifying materials by density).