Worksheet featuring 16 practice problems on calculating volume and density for different materials and objects.

Let’s solve each problem step by step. We’ll use the basic formula for density:

> Density = Mass ÷ Volume
> or rearranged:
> Mass = Density × Volume
> Volume = Mass ÷ Density

We’ll also remember that 1 cm³ = 1 mL, so we can treat them as the same unit when needed.

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Problem 1:
Platinum bar: 5.0 cm long, 4.0 cm wide, 1.5 cm thick. Mass = 700.0 g

a. Volume = length × width × height
= 5.0 × 4.0 × 1.5
= 20.0 × 1.5 = 30.0 cm³

b. Density = mass ÷ volume = 700.0 g ÷ 30.0 cm³ ≈ 23.33 g/cm³

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Problem 2:
Lead cylinder: mass = 540 g, density = 2.70 g/mL
Volume = mass ÷ density = 540 ÷ 2.70 = 200 mL (or cm³)

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Problem 3:
Cork: mass = 3 g, volume = 16 cm³
Density = 3 ÷ 16 = 0.1875 g/cm³

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Problem 4:
Glass bottle: holds 25 mL liquid, mass = 19 g
*(Note: This is ambiguous — does “mass of 19 grams” mean the bottle alone? Or bottle + liquid? But since it says “holds 25 ml of liquid and has a mass of 19 grams”, it likely means the bottle itself weighs 19g, but we’re asked to calculate density — probably of the liquid? Wait — no, it doesn’t give mass of liquid. Let me re-read.)*

Actually, rereading: “A thin glass bottle holds 25 ml of liquid and has a mass of 19 grams.” It doesn’t say what the 19g refers to. If it’s the mass of the empty bottle, we can’t find density of liquid without knowing its mass. If it’s the mass of the liquid, then:

Assume 19g is mass of liquid → Density = 19g / 25mL = 0.76 g/mL

But this is unclear. However, in many such problems, if they say “holds X ml and has mass Y”, they often mean the substance inside has mass Y. So we’ll go with that.

→ Density = 19g ÷ 25mL = 0.76 g/mL

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Problem 5:
Soap bar: 12 cm tall, 6 cm wide, 10 cm long → Volume = 12×6×10 = 720 cm³
Mass = 415 g
Density = 415 ÷ 720 ≈ 0.576 g/cm³

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Problem 6:
Metal sheet: 2 mm wide, 10 cm tall, 15 cm long → First convert all to same unit.

2 mm = 0.2 cm
Volume = 0.2 × 10 × 15 = 30 cm³
Mass = 4 g
Density = 4 ÷ 30 ≈ 0.133 g/cm³

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Problem 7:
Pencil: density = 0.875 g/mL, mass = 3.5 g
Volume = mass ÷ density = 3.5 ÷ 0.875 = 4.0 mL (cm³)

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Problem 8:
Water: volume = 50.0 mL, density = 1.00 g/mL
Mass = density × volume = 1.00 × 50.0 = 50.0 grams

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Problem 9:
Wood block: volume = 45.0 cm³, density = 0.65 g/mL
Mass = 0.65 × 45.0 = 29.25 grams

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Problem 10:
Rock: volume = 15 cm³, mass = 45 g
Density = 45 ÷ 15 = 3.0 g/cm³

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Problem 11:
Different rock: volume = 30 cm³, mass = 60 g
Density = 60 ÷ 30 = 2.0 g/cm³

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Problem 12:
Which rock is heavier? Rock #11 has mass 60g, Rock #10 has 45g → Rock #11 is heavier, Rock #10 is lighter

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Problem 13:
Which is denser? Rock #10: 3.0 g/cm³, Rock #11: 2.0 g/cm³ → Rock #10 is denser, Rock #11 is less dense

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Problem 14:
Boulder: cube, 30 cm on each side → Volume = 30×30×30 = 27,000 cm³
Density of granite = 2.8 g/cm³
Mass = density × volume = 2.8 × 27,000 = 75,600 grams = 75.6 kg

*(Since 1000g = 1kg)*

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Problem 15:
Basalt rock needs to weigh 2,000 kg → Convert to grams: 2,000 kg = 2,000,000 g
Density = 3200 kg/m³ → Convert to g/cm³:
3200 kg/m³ = 3.2 g/cm³ (since 1 g/cm³ = 1000 kg/m³)

Volume = mass ÷ density = 2,000,000 g ÷ 3.2 g/cm³ = 625,000 cm³

Or in m³: 625,000 cm³ = 0.625 m³ (since 1 m³ = 1,000,000 cm³)

But question asks “how big (what volume)” — so either is fine, but let’s give in cm³ as used earlier.

→ 625,000 cm³

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Problem 16:
Golden-colored cube: 2 cm on each side → Volume = 2×2×2 = 8 cm³
Mass = 40 g
Density = 40 ÷ 8 = 5.0 g/cm³

Gold’s density = 19.3 g/cm³ → This is NOT gold.

Should you buy it? No — it’s not gold, and paying $100 for something with density 5.0 g/cm³ (maybe pyrite or brass) is a bad deal.

→ Density = 5.0 g/cm³; Not gold; Do not buy

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Final Answer:

1a. 30.0 cm³
1b. 23.33 g/cm³
2. 200 mL
3. 0.1875 g/cm³
4. 0.76 g/mL
5. 0.576 g/cm³
6. 0.133 g/cm³
7. 4.0 mL
8. 50.0 g
9. 29.25 g
10. 3.0 g/cm³
11. 2.0 g/cm³
12. Rock #11 is heavier; Rock #10 is lighter
13. Rock #10 is denser; Rock #11 is less dense
14. 75.6 kg
15. 625,000 cm³
16. Density = 5.0 g/cm³; Not gold; Do not buy