Density free worksheet - Free Printable

Let’s solve each question step by step.

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Question 1: Which object is denser?

We are given mass and volume for four objects. Density is calculated using:

> Density = Mass / Volume

We’ll calculate the density for each object (in g/cm³ since mass is in grams and volume in cm³).

- Object A:
Density = 0.5 g / 0.1 cm³ = 5.0 g/cm³

- Object B:
Density = 10 g / 20 cm³ = 0.5 g/cm³

- Object C:
Density = 50 g / 75 cm³ ≈ 0.67 g/cm³

- Object D:
Density = 12 g / 13 cm³ ≈ 0.92 g/cm³

✔ Answer: Object A is the densest (5.0 g/cm³)

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Question 2: Which substance has the correct density?

We are given mass (kg), volume (m³), and a claimed density (g/cm³). We must check which one matches the actual density.

⚠️ Important unit conversion:
1 kg = 1000 g
1 m³ = 1,000,000 cm³ → So, 1 kg/m³ = 0.001 g/cm³

So to convert from kg/m³ to g/cm³, divide by 1000.

Alternatively, we can compute density in g/cm³ directly:

> Density (g/cm³) = [Mass (kg) × 1000] / [Volume (m³) × 1,000,000] = Mass (kg) / [Volume (m³) × 1000]

Let’s compute each:

- Substance A:
Mass = 10.0 kg, Volume = 3.0 m³
Density = 10.0 / (3.0 × 1000) = 10.0 / 3000 = 0.0033 g/cm³
But table says 0.33 g/cm³ → ✘ Incorrect

- Substance B:
Mass = 0.5 kg, Volume = 5.0 m³
Density = 0.5 / (5.0 × 1000) = 0.5 / 5000 = 0.0001 g/cm³
Table says 0.1 g/cm³ → ✘ Incorrect

- Substance C:
Mass = 6.0 kg, Volume = 24.0 m³
Density = 6.0 / (24.0 × 1000) = 6.0 / 24000 = 0.00025 g/cm³
Table says 4.0 g/cm³ → ✘ Incorrect

- Substance D:
Mass = 20.0 kg, Volume = 10.0 m³
Density = 20.0 / (10.0 × 1000) = 20.0 / 10000 = 0.002 g/cm³
Table says 0.5 g/cm³ → ✘ Incorrect

Wait — all seem wrong? Let’s double-check the problem.

Actually, let’s try computing density in kg/m³ first, then convert to g/cm³.

> Density (kg/m³) = Mass (kg) / Volume (m³)

Then convert to g/cm³:
Since 1 g/cm³ = 1000 kg/m³ → so divide kg/m³ by 1000 to get g/cm³.

- A: 10.0 / 3.0 = 3.333 kg/m³ → 3.333 / 1000 = 0.00333 g/cm³ ≠ 0.33 → ✘
- B: 0.5 / 5.0 = 0.1 kg/m³ → 0.1 / 1000 = 0.0001 g/cm³ ≠ 0.1 → ✘
- C: 6.0 / 24.0 = 0.25 kg/m³ → 0.25 / 1000 = 0.00025 g/cm³ ≠ 4.0 → ✘
- D: 20.0 / 10.0 = 2.0 kg/m³ → 2.0 / 1000 = 0.002 g/cm³ ≠ 0.5 → ✘

All are incorrect? That can’t be right.

Wait — perhaps there’s a mistake in the table or units. Maybe the density column is meant to be in kg/m³, not g/cm³?

Let’s test that.

If density is in kg/m³, then:

- A: 10.0 kg / 3.0 m³ = 3.33 kg/m³ → but table says 0.33 → ✘
- B: 0.5 / 5.0 = 0.1 kg/m³ → table says 0.1 → ✔ Matches!
- C: 6.0 / 24.0 = 0.25 kg/m³ → table says 4.0 → ✘
- D: 20.0 / 10.0 = 2.0 kg/m³ → table says 0.5 → ✘

So if the density column is in kg/m³, then Substance B is correct.

But the column header says Density (g/cm³) — which makes B still wrong.

However, 0.1 g/cm³ = 100 kg/m³, and 0.5 kg / 5.0 m³ = 0.1 kg/m³ → which is 0.0001 g/cm³ — doesn’t match.

Wait — maybe the mass is in grams, not kg? But it says “Mass (kg)”.

This seems like an error in the worksheet.

But let’s look again — perhaps they forgot to convert units.

Suppose we ignore the unit label and just check consistency.

Compute density as mass/volume with given numbers, assuming the density column is supposed to match that.

For Substance B:
Mass = 0.5, Volume = 5.0 → Density = 0.5 / 5.0 = 0.1 → matches the given density of 0.1.

Similarly:

- A: 10.0 / 3.0 ≈ 3.33 ≠ 0.33
- C: 6.0 / 24.0 = 0.25 ≠ 4.0
- D: 20.0 / 10.0 = 2.0 ≠ 0.5

Only B gives a matching numerical value.

So likely, the units are inconsistent, but numerically, Substance B is the only one where density = mass/volume (ignoring units).

✔ Answer: Substance B (assuming the density column is meant to be consistent numerically, even if units are mislabeled)

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Question 3: What is the density of the stones?

Given:

- Total mass of two stones = 50 grams
- Initial water volume = 30 cm³
- Final water volume = 40 cm³

→ Volume displaced by stones = 40 - 30 = 10 cm³

This is the volume of the stones.

Density = Mass / Volume = 50 g / 10 cm³ = 5.0 g/cm³

✔ Answer: C. 5.0 g/cm³

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## ✔ Final Answers:

1. Object A is the densest.
2. Substance B has the correct density (numerically, despite unit inconsistency).
3. C. 5.0 g/cm³

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