Practice Sheet Calculating Density | PDF | Density | Volume - Free Printable

Let's solve each problem on the Density Calculations Worksheet step by step. The formula for density is:

$$
\text{Density} = \frac{\text{Mass}}{\text{Volume}}
$$

We'll use this formula and its rearrangements:
- $ \text{Mass} = \text{Density} \times \text{Volume} $
- $ \text{Volume} = \frac{\text{Mass}}{\text{Density}} $

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1) A student measures the mass of an 8 cm³ block of brown sugar to be 12.9 g. What is the density of the brown sugar?

Given:
- Mass = 12.9 g
- Volume = 8 cm³

$$
\text{Density} = \frac{12.9\ \text{g}}{8\ \text{cm}^3} = 1.6125\ \text{g/cm}^3
$$

✔ Answer: 1.61 g/cm³ (rounded to two decimal places)

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2) A chef fills a 50 mL container with 43.5 g of cooking oil. What is the density of the oil?

Given:
- Mass = 43.5 g
- Volume = 50 mL

Note: 1 mL = 1 cm³, so we can use g/mL.

$$
\text{Density} = \frac{43.5\ \text{g}}{50\ \text{mL}} = 0.87\ \text{g/mL}
$$

✔ Answer: 0.87 g/mL

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3) Calculate the mass of a liquid with a density of 2.5 g/mL and a volume of 15 mL.

Given:
- Density = 2.5 g/mL
- Volume = 15 mL

$$
\text{Mass} = \text{Density} \times \text{Volume} = 2.5\ \text{g/mL} \times 15\ \text{mL} = 37.5\ \text{g}
$$

✔ Answer: 37.5 g

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4) Calculate the volume of a liquid with a density of 5.45 g/mL and a mass of 65 g.

Given:
- Density = 5.45 g/mL
- Mass = 65 g

$$
\text{Volume} = \frac{\text{Mass}}{\text{Density}} = \frac{65\ \text{g}}{5.45\ \text{g/mL}} \approx 11.93\ \text{mL}
$$

✔ Answer: 11.9 mL (rounded to one decimal place)

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5) A machine shop worker records the mass of an aluminum cube as 176 g. If one side of the cube measures 4 cm, what is the density of the aluminum?

First, find the volume of the cube:

$$
\text{Volume} = \text{side}^3 = 4\ \text{cm} \times 4\ \text{cm} \times 4\ \text{cm} = 64\ \text{cm}^3
$$

Now calculate density:

$$
\text{Density} = \frac{176\ \text{g}}{64\ \text{cm}^3} = 2.75\ \text{g/cm}^3
$$

✔ Answer: 2.75 g/cm³

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6) A teacher performing a demonstration finds that a piece of cork displaces 23.5 mL of water. The piece of cork has a mass of 5.7 g. What is the density of the cork?

Displacement = Volume of cork = 23.5 mL = 23.5 cm³
Mass = 5.7 g

$$
\text{Density} = \frac{5.7\ \text{g}}{23.5\ \text{cm}^3} \approx 0.2426\ \text{g/cm}^3
$$

✔ Answer: 0.24 g/cm³ (rounded to two significant figures)

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7) A carver begins work on the following block of granite that weighs 2700 g. What is the density of the granite?

From the diagram:
- Length = 20 cm
- Width = 5 cm
- Height = 10 cm

$$
\text{Volume} = 20 \times 5 \times 10 = 1000\ \text{cm}^3
$$

Mass = 2700 g

$$
\text{Density} = \frac{2700\ \text{g}}{1000\ \text{cm}^3} = 2.7\ \text{g/cm}^3
$$

✔ Answer: 2.7 g/cm³

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8) A piece of PVC plumbing pipe displaces 60 mL when placed into a container of water. If the pipe has a mass of 78 g, what is the density of PVC?

Displacement = Volume = 60 mL = 60 cm³
Mass = 78 g

$$
\text{Density} = \frac{78\ \text{g}}{60\ \text{cm}^3} = 1.3\ \text{g/cm}^3
$$

✔ Answer: 1.3 g/cm³

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9) A solid magnesium flare has a mass of 1300 g and a volume of 743 cm³. What is the density of the magnesium?

Given:
- Mass = 1300 g
- Volume = 743 cm³

$$
\text{Density} = \frac{1300\ \text{g}}{743\ \text{cm}^3} \approx 1.75\ \text{g/cm}^3
$$

✔ Answer: 1.75 g/cm³

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✔ Final Answers Summary:

| Problem | Answer |
|--------|--------|
| 1 | 1.61 g/cm³ |
| 2 | 0.87 g/mL |
| 3 | 37.5 g |
| 4 | 11.9 mL |
| 5 | 2.75 g/cm³ |
| 6 | 0.24 g/cm³ |
| 7 | 2.7 g/cm³ |
| 8 | 1.3 g/cm³ |
| 9 | 1.75 g/cm³ |

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