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:

> Density (d) = Mass (M) / Volume (V)

Let’s go through each section and verify the solutions, then explain the reasoning step-by-step.

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🔷 Section 1: Find the unknown quantity

We use the formula:
- $ d = \frac{M}{V} $
- $ M = d \times V $
- $ V = \frac{M}{d} $

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

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

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

$$
d = \frac{M}{V} = \frac{95\ \text{g}}{950\ \text{mL}} = 0.1\ \text{g/mL}
$$
✔ Correct: d = 0.1 g/mL

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

$$
V = \frac{M}{d} = \frac{20\ \text{g}}{0.5\ \text{g/cm}^3} = 40\ \text{cm}^3
$$
✔ Correct: V = 40 cm³

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🔷 Section 2: Find the unknown quantity (convert first to g or mL)

We need to convert units before applying the formula.

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

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

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

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

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

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

Note: This value is very small, which makes sense because 500 mg is only 0.5 grams in 520 mL — a very low-density substance.

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🔷 Word Problem

> 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} $

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

✔ Correct: d = 2.7 g/mL

This matches the known density of aluminum (~2.7 g/mL), so it's a good check!

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✔ Summary of All Answers

| Question | 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 |

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📌 Key Concepts & Tips

1. Density Formula:
Always remember:
$$
\text{Density} = \frac{\text{Mass}}{\text{Volume}}
$$

2. Units Matter!
- For solids: g/cm³
- For liquids: g/mL
- Note: 1 mL = 1 cm³, so they are equivalent.

3. Unit Conversions:
- 1 L = 1000 mL
- 1 kg = 1000 g
- 1 g = 1000 mg

4. Use the triangle method (shown at top right):
- Cover the variable you want:
- If you cover M, you get d × V
- If you cover d, you get M ÷ V
- If you cover V, you get M ÷ d

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✔ Final Thoughts

All calculations in the worksheet are correctly solved. The student has applied the density formula properly and handled unit conversions accurately.

If this were a homework assignment, the work shown would receive full credit — clear steps, correct math, proper units, and logical reasoning.

Let me know if you'd like a version of this with explanations formatted as a study guide or quiz review!