Handwritten solutions to a density calculations worksheet, showing step-by-step problem-solving for mass, volume, and density.

Let's go through the Density Calculations Worksheet step by step and solve each problem with explanations.

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🔷 Key Formula:

> Density = Mass / Volume
> Units:
> - Solids: g/cm³
> - Liquids: g/mL

Also, remember:
- 1 mL = 1 cm³
- 1 kg = 1000 g
- 1 L = 1000 mL

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## ✔ Part 1: Find the unknown quantity

a)

Given:
- Density (d) = 3 g/mL
- Volume (V) = 10 mL
Find: Mass (m)

Use:
> m = d × V
> m = 3 g/mL × 10 mL = 30 g

✔ Answer: 30 g

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b)

Given:
- Mass (m) = 95 g
- Volume (V) = 10 mL
Find: Density (d)

Use:
> d = m / V
> d = 95 g / 10 mL = 9.5 g/mL

✔ Answer: 9.5 g/mL

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c)

Given:
- Density (d) = 0.5 g/cm³
- Mass (m) = 10 g
Find: Volume (V)

Use:
> V = m / d
> V = 10 g / 0.5 g/cm³ = 20 cm³

✔ Answer: 20 cm³

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## ✔ Part 2: Find the unknown quantity (CONVERT FIRST to g or mL)

a)

Given:
- Mass = 6.5 kg
- Volume = 200 mL
Find: Density

Convert mass to grams:
> 6.5 kg = 6.5 × 1000 = 6500 g

Now use:
> d = m / V = 6500 g / 200 mL = 32.5 g/mL

✔ Answer: 32.5 g/mL

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b)

Given:
- Mass = 1.5 kg
- Volume = 1000 mL
Find: Density

Convert mass:
> 1.5 kg = 1500 g

> d = 1500 g / 1000 mL = 1.5 g/mL

✔ Answer: 1.5 g/mL

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c)

Given:
- Mass = 521 g
- Volume = 220 mL
Find: Density

> d = 521 g / 220 mL ≈ 2.37 g/mL

(You can round to 2 decimal places.)

✔ Answer: 2.37 g/mL

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## ✔ WORD PROBLEMS

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

Use:
> d = m / V = 40.5 g / 15.0 mL = 2.7 g/mL

✔ Answer: 2.7 g/mL

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2. Mercury metal is poured into a graduated cylinder that holds 22.5 mL. The mercury used to fill the cylinder weighs 305.0 g. From this information, calculate the density of mercury.

> d = m / V = 305.0 g / 22.5 mL ≈ 13.56 g/mL

(Rounded to two decimal places.)

✔ Answer: 13.56 g/mL

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📌 Summary of Answers:

#### Part 1:
a) 30 g
b) 9.5 g/mL
c) 20 cm³

#### Part 2:
a) 32.5 g/mL
b) 1.5 g/mL
c) 2.37 g/mL

#### Word Problems:
1) 2.7 g/mL
2) 13.56 g/mL

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