Science 8 - Density Calculations Worksheet with handwritten solutions showing step-by-step problem-solving for calculating density, mass, and volume.

The image you've uploaded is a completed Density Calculations Worksheet for Science 8, with all problems solved and answers provided. Below is a detailed explanation of each problem and its solution, along with verification of the calculations.

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🔍 Density Formula:

$$
\text{Density (D)} = \frac{\text{Mass (m)}}{\text{Volume (V)}}
$$

Units commonly used:
- Mass: grams (g)
- Volume: cm³ or mL (note: 1 mL = 1 cm³)
- Density: g/cm³ or g/mL

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✔ Problem-by-Problem Explanation:

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#### 1) Brown Sugar Density
- Given:
- Mass (m) = 12.9 g
- Volume (V) = 8 cm³
- Solve:
$$
D = \frac{12.9\ \text{g}}{8\ \text{cm}^3} = 1.6125\ \text{g/cm}^3
$$
✔ Correct answer: 1.6125 g/cm³

> ✔️ This is correct. The student divided mass by volume properly.

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#### 2) Cooking Oil Density
- Given:
- Mass (m) = 43.5 g
- Volume (V) = 50 mL
- Solve:
$$
D = \frac{43.5\ \text{g}}{50\ \text{mL}} = 0.87\ \text{g/mL}
$$
✔ Correct answer: 0.87 g/mL

> ✔️ Correct calculation. Note that mL and cm³ are equivalent.

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#### 3) Mass of Liquid
- Given:
- Density (D) = 2.5 g/mL
- Volume (V) = 15 mL
- Use rearranged formula:
$$
m = D \times V = 2.5\ \text{g/mL} \times 15\ \text{mL} = 37.5\ \text{g}
$$
✔ Correct answer: 37.5 g

> ✔️ Correct. Used the formula properly.

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#### 4) Volume of Liquid
- Given:
- Density (D) = 5.45 g/mL
- Mass (m) = 65 g
- Rearranged formula:
$$
V = \frac{m}{D} = \frac{65\ \text{g}}{5.45\ \text{g/mL}} \approx 11.93\ \text{mL}
$$
✔ Answer given: 11.93 mL → ✔️ Correct

> ✔️ Rounded to two decimal places appropriately.

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#### 5) Aluminum Cube Density
- Given:
- Mass (m) = 176 g
- Side length = 4 cm → cube
- Volume of cube:
$$
V = s^3 = 4 \times 4 \times 4 = 64\ \text{cm}^3
$$
- Density:
$$
D = \frac{176\ \text{g}}{64\ \text{cm}^3} = 2.75\ \text{g/cm}^3
$$
✔ Correct answer: 2.75 g/cm³

> ✔️ Correct. Standard density of aluminum is ~2.7 g/cm³ — this is close and reasonable.

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#### 6) Cork Density
- Given:
- Mass (m) = 5.7 g
- Displaces 23.5 mL of water → Volume = 23.5 mL
- So:
$$
D = \frac{5.7\ \text{g}}{23.5\ \text{mL}} \approx 0.2426\ \text{g/mL} \approx 0.24\ \text{g/mL}
$$
✔ Answer given: 0.24 g/mL → ✔️ Correct

> ✔️ Good approximation (rounded to two significant figures).

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#### 7) Granite Block Density
- Given:
- Mass (m) = 2700 g
- Dimensions: 20 cm × 10 cm × 5 cm
- Volume:
$$
V = L \times W \times H = 20 \times 10 \times 5 = 1000\ \text{cm}^3
$$
- Density:
$$
D = \frac{2700\ \text{g}}{1000\ \text{cm}^3} = 2.7\ \text{g/cm}^3
$$
✔ Answer given: 2.7 g/cm³ → ✔️ Correct

> ✔️ Matches known density of granite (~2.6–2.8 g/cm³)

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#### 8) PVC Pipe Density
- Given:
- Mass (m) = 78 g
- Displaces 60 mL → Volume = 60 mL
- Density:
$$
D = \frac{78\ \text{g}}{60\ \text{mL}} = 1.3\ \text{g/mL}
$$
✔ Answer given: 1.3 g/mL → ✔️ Correct

> ✔️ Simple division; correct rounding.

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#### 9) Magnesium Bar Density
- Given:
- Mass (m) = 1300 g
- Volume (V) = 743 cm³
- Density:
$$
D = \frac{1300\ \text{g}}{743\ \text{cm}^3} \approx 1.749\ \text{g/cm}^3 \approx 1.75\ \text{g/cm}^3
$$
✔ Answer given: 1.75 g/cm³ → ✔️ Correct

> ✔️ Rounded to three significant figures.

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✔ Final Summary:

All problems on the worksheet have been correctly solved, and the answers are accurate based on the formulas and data provided.

🧠 Key Takeaways:

- Always use:
$$
D = \frac{m}{V},\quad m = D \times V,\quad V = \frac{m}{D}
$$
- Units must match (e.g., g and cm³ or g and mL).
- For irregular solids, use water displacement to find volume.
- For cubes or rectangular prisms, use $ V = L \times W \times H $.

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