Density Calculations online exercise for - Free Printable

Absolutely! Let’s solve this Density Calculations Worksheet I step by step, explaining each part clearly.

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## 🔢 FORMULAS TO REMEMBER:
- density (d) = mass (M) / volume (V) → `d = M/V`
- Rearranged:
- mass (M) = density (d) × volume (V) → `M = d × V`
- volume (V) = mass (M) / density (d) → `V = M/d`

> ✔ Units:
> - Solids → g/cm³
> - Liquids → g/mL
> *(Note: 1 mL = 1 cm³, so these units are interchangeable)*

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# 🧮 SECTION 1: Find the unknown quantity

a) d = 3 g/mL, V = 100 mL, M = ?

Use: M = d × V

→ M = 3 g/mL × 100 mL = 300 g

✔ Answer: M = 300 g

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b) d = ?, V = 95 mL, M = 950 g

Use: d = M / V

→ d = 950 g / 95 mL = 10 g/mL

✔ Answer: d = 10 g/mL

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c) d = 5 g/cm³, V = ?, M = 20 g

Use: V = M / d

→ V = 20 g / 5 g/cm³ = 4 cm³

✔ Answer: V = 4 cm³

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# 🧮 SECTION 2: Find the unknown quantity

a) d = 24 g/mL, V = 2 mL, M = ?

→ M = 24 g/mL × 2 mL = 48 g

✔ Answer: M = 48 g

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b) d = ?, V = 10 mL, M = 150 g

→ d = 150 g / 10 mL = 15 g/mL

✔ Answer: d = 15 g/mL

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c) d = ?, V = 50 mL, M = 500 g

→ d = 500 g / 50 mL = 10 g/mL

✔ Answer: d = 10 g/mL

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# 📖 WORD PROBLEMS

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1. A block of aluminum occupies a volume of 15 mL and weighs 45 g. What is its density?

→ d = M / V = 45 g / 15 mL = 3 g/mL

✔ Answer: 3 g/mL

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2. Mercury metal is poured into a graduated cylinder that holds exactly 20 mL. The mercury used to fill the cylinder weighs 400 g. From this information, calculate the density of mercury.

→ d = M / V = 400 g / 20 mL = 20 g/mL

✔ Answer: 20 g/mL

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3. A rectangular block of metal weighs 3200 g. The dimensions of the block are 8 cm by 5 cm by 4 cm. From this data, what is the density of the metal? (hint: find the volume of a block first)

→ First, find volume:
V = length × width × height = 8 cm × 5 cm × 4 cm = 160 cm³

→ Now, density:
d = M / V = 3200 g / 160 cm³ = 20 g/cm³

✔ Answer: 20 g/cm³

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4. What volume of silver metal will weigh exactly 2500.0 g? The density of silver is 10.5 g/cm³.

→ Use: V = M / d

→ V = 2500.0 g / 10.5 g/cm³ ≈ 238.1 cm³ *(rounded to one decimal place)*

✔ Answer: 238.1 cm³

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5. A block of lead has dimensions of 4.5 cm by 5.2 cm by 6.0 cm. The block weighs 1587 g. From this information, calculate the density of lead.

→ First, find volume:
V = 4.5 cm × 5.2 cm × 6.0 cm
= (4.5 × 5.2) = 23.4 → then × 6.0 = 140.4 cm³

→ Now, density:
d = M / V = 1587 g / 140.4 cm³ ≈ 11.3 g/cm³ *(rounded to one decimal place)*

✔ Answer: 11.3 g/cm³

*(This matches the known density of lead, which is about 11.34 g/cm³ — great job!)*

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## ✔ FINAL ANSWERS SUMMARY:

Section 1:

a) M = 300 g
b) d = 10 g/mL
c) V = 4 cm³

Section 2:

a) M = 48 g
b) d = 15 g/mL
c) d = 10 g/mL

Word Problems:

1. 3 g/mL
2. 20 g/mL
3. 20 g/cm³
4. 238.1 cm³
5. 11.3 g/cm³

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