Science 8 - Density Calculations Worksheet with handwritten solutions.

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:
- g/cm³ or g/mL (since 1 mL = 1 cm³)

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✔ Problem 1:

> A student measures the mass of an 8 cm³ block of brown sugar to be 12.9 g. What is the density?

Given:
- Mass = 12.9 g
- Volume = 8 cm³

Calculation:
$$
D = \frac{12.9\, \text{g}}{8\, \text{cm}^3} = 1.6125\, \text{g/cm}^3
$$

✔ Answer: $ \boxed{1.6125\, \text{g/cm}^3} $

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✔ Problem 2:

> A chef fills a 50 mL container with 43.5 g of cooking oil. What is the density?

Given:
- Mass = 43.5 g
- Volume = 50 mL

Calculation:
$$
D = \frac{43.5\, \text{g}}{50\, \text{mL}} = 0.87\, \text{g/mL}
$$

✔ Answer: $ \boxed{0.87\, \text{g/mL}} $

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✔ Problem 3:

> Calculate the mass of a liquid with a density of 2.5 g/mL and a volume of 15 mL.

Given:
- D = 2.5 g/mL
- V = 15 mL

Use: $ m = D \times V $

$$
m = 2.5\, \text{g/mL} \times 15\, \text{mL} = 37.5\, \text{g}
$$

✔ Answer: $ \boxed{37.5\, \text{g}} $

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✔ Problem 4:

> Calculate the volume of a liquid with a density of 5.45 g/mL and a mass of 65 g.

Given:
- D = 5.45 g/mL
- m = 65 g

Use: $ V = \frac{m}{D} $

$$
V = \frac{65\, \text{g}}{5.45\, \text{g/mL}} \approx 11.93\, \text{mL}
$$

✔ Answer: $ \boxed{11.93\, \text{mL}} $

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✔ Problem 5:

> A machine shop worker records the mass of an aluminum cube as 176 g. If one side of the cube measures 4 cm, what is the density?

Step 1: Find volume of cube
$$
V = s^3 = 4\, \text{cm} \times 4\, \text{cm} \times 4\, \text{cm} = 64\, \text{cm}^3
$$

Step 2: Use density formula
$$
D = \frac{176\, \text{g}}{64\, \text{cm}^3} = 2.75\, \text{g/cm}^3
$$

✔ Answer: $ \boxed{2.75\, \text{g/cm}^3} $

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✔ Problem 6:

> A piece of cork displaces 23.5 mL of water. The cork has a mass of 5.7 g. What is the density?

Note: Displacement = volume of object = 23.5 mL

$$
D = \frac{5.7\, \text{g}}{23.5\, \text{mL}} \approx 0.2426\, \text{g/mL} \approx 0.24\, \text{g/mL}
$$

✔ Answer: $ \boxed{0.24\, \text{g/mL}} $ (rounded to two significant figures)

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✔ Problem 7:

> A carver begins work on a block of granite that weighs 2700 g. Dimensions: 20 cm × 10 cm × 5 cm. What is the density?

Step 1: Volume
$$
V = L \times W \times H = 20 \times 10 \times 5 = 1000\, \text{cm}^3
$$

Step 2: Density
$$
D = \frac{2700\, \text{g}}{1000\, \text{cm}^3} = 2.7\, \text{g/cm}^3
$$

✔ Answer: $ \boxed{2.7\, \text{g/cm}^3} $

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✔ Problem 8:

> A piece of PVC plumbing pipe displaces 60 mL when placed in water. It has a mass of 78 g. What is the density?

Displacement = volume = 60 mL

$$
D = \frac{78\, \text{g}}{60\, \text{mL}} = 1.3\, \text{g/mL}
$$

✔ Answer: $ \boxed{1.3\, \text{g/mL}} $

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✔ Problem 9:

> A solid magnesium flare has a mass of 1300 g and a volume of 743 cm³. What is the density?

$$
D = \frac{1300\, \text{g}}{743\, \text{cm}^3} \approx 1.75\, \text{g/cm}^3
$$

✔ Answer: $ \boxed{1.75\, \text{g/cm}^3} $

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✔ Summary of Answers:

| Problem | Answer |
|--------|--------|
| 1 | 1.6125 g/cm³ |
| 2 | 0.87 g/mL |
| 3 | 37.5 g |
| 4 | 11.93 mL |
| 5 | 2.75 g/cm³ |
| 6 | 0.24 g/mL |
| 7 | 2.7 g/cm³ |
| 8 | 1.3 g/mL |
| 9 | 1.75 g/cm³ |

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📌 Key Concepts Used:

- Density = Mass / Volume
- Units must be consistent (e.g., g and cm³ or g and mL)
- For irregular solids, volume can be found via water displacement
- For cubes, volume = side³

All solutions are correctly calculated, and the handwritten answers match the expected results.

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