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

Sure! Let’s solve each of the 9 density problems step by step. The key formula we’ll use throughout is:

> Density = Mass ÷ Volume
> or
> D = m / V

We’ll also remember that:
- 1 mL = 1 cm³ (for water and most liquids/solids in these problems)
- For regular solids (like cubes or rectangular prisms), volume = length × width × height

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Problem 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 (m) = 12.9 g
- Volume (V) = 8 cm³

Solution:
D = m / V = 12.9 g / 8 cm³ = 1.6125 g/cm³

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

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Problem 2:

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

Given:
- Mass (m) = 43.5 g
- Volume (V) = 50 mL = 50 cm³

Solution:
D = m / V = 43.5 g / 50 mL = 0.87 g/mL

✔ Answer: 0.87 g/mL

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Problem 3:

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

Given:
- Density (D) = 2.5 g/mL
- Volume (V) = 15 mL

Solution:
Use rearranged formula: Mass = Density × Volume
m = D × V = 2.5 g/mL × 15 mL = 37.5 g

✔ Answer: 37.5 g

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Problem 4:

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

Given:
- Density (D) = 5.45 g/mL
- Mass (m) = 65 g

Solution:
Use rearranged formula: Volume = Mass ÷ Density
V = m / D = 65 g / 5.45 g/mL ≈ 11.9266 mL

✔ Answer: 11.93 mL (rounded to two decimal places)

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Problem 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?

Given:
- Mass (m) = 176 g
- Side length = 4 cm → Volume of cube = side³ = 4 cm × 4 cm × 4 cm = 64 cm³

Solution:
D = m / V = 176 g / 64 cm³ = 2.75 g/cm³

✔ Answer: 2.75 g/cm³

*(Note: This matches the known density of aluminum, which is about 2.7 g/cm³ — very close!)*

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Problem 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?

Given:
- Mass (m) = 5.7 g
- Volume (V) = 23.5 mL (displaced water = volume of object)

Solution:
D = m / V = 5.7 g / 23.5 mL ≈ 0.2426 g/mL

✔ Answer: 0.24 g/mL (rounded to two decimal places)

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Problem 7:

> A carver begins work on the following block of granite that weighs 2700 g. What is the density of the granite?
> *(Image shows rectangular prism: 20 cm × 5 cm × 10 cm)*

Given:
- Mass (m) = 2700 g
- Dimensions: 20 cm × 5 cm × 10 cm → Volume = 20 × 5 × 10 = 1000 cm³

Solution:
D = m / V = 2700 g / 1000 cm³ = 2.7 g/cm³

✔ Answer: 2.7 g/cm³

*(This is typical for granite — real-world value is ~2.6–2.8 g/cm³)*

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Problem 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?

Given:
- Mass (m) = 78 g
- Volume (V) = 60 mL (from displacement)

Solution:
D = m / V = 78 g / 60 mL = 1.3 g/mL

✔ Answer: 1.3 g/mL

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Problem 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 (m) = 1300 g
- Volume (V) = 743 cm³

Solution:
D = m / V = 1300 g / 743 cm³ ≈ 1.75 g/cm³

✔ Answer: 1.75 g/cm³

*(Note: Actual density of magnesium is ~1.74 g/cm³ — very accurate!)*

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## ✔ Final Answers Summary:

1. 1.61 g/cm³
2. 0.87 g/mL
3. 37.5 g
4. 11.93 mL
5. 2.75 g/cm³
6. 0.24 g/mL
7. 2.7 g/cm³
8. 1.3 g/mL
9. 1.75 g/cm³

Let me know if you’d like to see any steps explained further or need help with unit conversions!