Th Grade Science Density Worksheet Record All Your Work On - Fill ... - Free Printable

It looks like you've uploaded a "Grade Science Density Worksheet" with 13 problems related to density, mass, volume, and calculations. Since I can't view images directly, I’ll solve each problem step by step based on the text you provided.

Let me go through each question carefully, apply the formula:

> Density = Mass / Volume

and solve accordingly. I'll also explain each solution clearly.

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1. State the formula for density (in words and mathematical symbols).

- In words: Density equals mass divided by volume.
- Mathematical symbol:
$$
\rho = \frac{m}{V}
$$

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2. A rock has a mass of 120 grams and occupies a volume of 70 cm³. What is its density?

$$
\text{Density} = \frac{\text{Mass}}{\text{Volume}} = \frac{120\ \text{g}}{70\ \text{cm}^3} = 1.714\ \text{g/cm}^3
$$

✔ Answer: ≈ 1.71 g/cm³

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3. An unknown liquid occupies a volume of 5 mL and has a mass of 40 grams. Find its density.

Note: 1 mL = 1 cm³

$$
\text{Density} = \frac{40\ \text{g}}{5\ \text{mL}} = 8\ \text{g/mL}
$$

✔ Answer: 8 g/mL

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4. Define the following vocabulary words:

a) Mass – The amount of matter in an object, measured in grams (g) or kilograms (kg).

b) Volume – The amount of space an object occupies, measured in cm³, mL, or m³.

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5. How does the following concept apply to a cubic centimeter (cm³) compared with a volume occupied by a milliliter (mL)?

→ They are equivalent.
1 cm³ = 1 mL
So, a cubic centimeter and a milliliter measure the same volume.

✔ Answer: A cubic centimeter (cm³) is equal in volume to a milliliter (mL).

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6. A rectangular solid of unknown density is 5 meters long, 2 meters high and 4 meters wide. The mass of this solid is 300 grams. Give both: information for the calculation (label), and then calculate the density.

First, find volume:
$$
V = \text{length} \times \text{width} \times \text{height} = 5\ \text{m} \times 2\ \text{m} \times 4\ \text{m} = 40\ \text{m}^3
$$

But mass is given as 300 grams, which is very small for a 40 m³ object. That seems inconsistent.

Wait — likely a unit error. Probably the mass should be 300 kg or 300,000 grams, but let’s proceed with what's written.

Convert mass to kilograms or check units.

But let’s assume it's 300 grams = 0.3 kg

Then:
$$
\text{Density} = \frac{0.3\ \text{kg}}{40\ \text{m}^3} = 0.0075\ \text{kg/m}^3
$$

Or in g/cm³:
- 40 m³ = 40 × 10⁶ cm³ = 40,000,000 cm³
- Mass = 300 g

$$
\text{Density} = \frac{300\ \text{g}}{40,000,000\ \text{cm}^3} = 0.0000075\ \text{g/cm}^3
$$

This is extremely low (like less than air). So likely a typo.

But since the problem says 300 grams, we must use that.

✔ Answer:
- Volume = 40 m³
- Mass = 300 g = 0.3 kg
- Density = 0.3 kg / 40 m³ = 0.0075 kg/m³

But more realistically, perhaps the mass was meant to be 300 kg?

Let’s suppose it's 300 kg:

Then:
$$
\text{Density} = \frac{300\ \text{kg}}{40\ \text{m}^3} = 7.5\ \text{kg/m}^3
$$

Still low (less than water), but possible.

But without correction, we stick to given values.

✔ Final answer (based on given data):
- Volume: 40 m³
- Mass: 300 g = 0.3 kg
- Density: 0.0075 kg/m³

(But note: This suggests a typo — possibly mass is 300,000 g or 300 kg.)

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7. A rock occupies a volume of 20 cm³ and has a mass of 54 grams. Find the density of this rock.

$$
\text{Density} = \frac{54\ \text{g}}{20\ \text{cm}^3} = 2.7\ \text{g/cm}^3
$$

✔ Answer: 2.7 g/cm³

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8. A rock has a density of 4 g/mL and a mass of 10 grams. What is the volume this rock occupies?

Use:
$$
V = \frac{m}{\rho} = \frac{10\ \text{g}}{4\ \text{g/mL}} = 2.5\ \text{mL}
$$

✔ Answer: 2.5 mL

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9. An unknown substance from planet X has a density of 10 g/mL. It occupies a volume of 80 mL. What is the mass of this substance (in grams)?

$$
m = \rho \times V = 10\ \text{g/mL} \times 80\ \text{mL} = 800\ \text{g}
$$

✔ Answer: 800 grams

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10. When a cube is density of 1.0 g/cm³, and crown when has a density of 1.025 g/cm³. Why are they different?

Wait — probably typo.

Likely: "When a cube of aluminum has a density of 1.0 g/cm³, and a crown made of gold has a density of 1.025 g/cm³..." — but that doesn’t make sense because aluminum is ~2.7 g/cm³, gold is ~19.3 g/cm³.

Possibly meant:
"A cube of ice has a density of 0.9 g/cm³, and a crown made of gold has a density of 19.3 g/cm³."

But based on what’s written:

→ If two objects have different densities, it means they are made of different materials or have different compositions.

Even if they look similar, their densities differ due to atomic structure, packing, etc.

✔ Answer: They are different because they are made of different materials (or have different internal structures), so the mass per unit volume varies.

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11. A cube made of an unknown material has a height of 9 cm. The mass of this cube is 3,645 grams. Calculate the density of this cube (give the information).

First, find volume.

Since it’s a cube:
$$
\text{Side length} = 9\ \text{cm}
$$
$$
V = s^3 = 9^3 = 729\ \text{cm}^3
$$

Mass = 3,645 g

$$
\text{Density} = \frac{3,645\ \text{g}}{729\ \text{cm}^3} = 5\ \text{g/cm}^3
$$

✔ Answer: Density = 5 g/cm³

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12. Given a large bucket of water at room temperature (20°C), show the approximate position of the following objects when placed in the bucket of water and explain why you placed them as you did. (Draw lines down middle of water and label approximating position you place them in.)

We are told to draw, but since we can’t draw here, I’ll describe the positions.

#### a) Ice (D = 0.92 g/mL)

- Ice has density less than water (1.0 g/mL)
- So it floats on top.

✔ Position: Floating on surface

#### b) Wood (D = 0.6 g/mL)

- Less dense than water → floats

✔ Position: Floating on surface

#### c) Aluminum (D = 2.7 g/mL)

- More dense than water → sinks

✔ Position: Sinks to bottom

#### d) Iron (D = 7.9 g/mL)

- Much denser than water → sinks

✔ Position: Sinks to bottom

#### e) Gold (D = 19.3 g/mL)

- Very dense → sinks

✔ Position: Sinks to bottom

Explanation: Objects with density less than 1.0 g/mL float; those with greater than 1.0 g/mL sink.

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✔ Final Summary of Answers:

| Question | Answer |
|--------|--------|
| 1 | Density = Mass / Volume; ρ = m/V |
| 2 | 1.71 g/cm³ |
| 3 | 8 g/mL |
| 4a | Mass: amount of matter |
| 4b | Volume: space occupied |
| 5 | 1 cm³ = 1 mL |
| 6 | Volume = 40 m³, Mass = 300 g → Density = 0.0075 kg/m³ *(note: likely typo in mass)* |
| 7 | 2.7 g/cm³ |
| 8 | 2.5 mL |
| 9 | 800 g |
| 10 | Different materials → different densities |
| 11 | 5 g/cm³ |
| 12 | Ice & wood float; Al, iron, gold sink |

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Let me know if you'd like a printable version or help drawing the diagram for #12!