Finding Mass and Volume from the Density Formula Worksheet #1 - Free Printable

Problem: Solving the Density Formula Worksheet

The density formula is given by:
\[
\text{Density} = \frac{\text{Mass}}{\text{Volume}}
\]
Rearranging this formula, we can solve for mass or volume as needed:
1. Mass = Density × Volume
2. Volume = Mass ÷ Density

Let's solve each problem step by step.

---

Problem 1:

The volume of a block of plastic is \(2 \, \text{cm} \times 4 \, \text{cm} \times 5 \, \text{cm}\). If the density of the plastic is \(2 \, \text{g/cm}^3\), what is the mass of the plastic block?

#### Step 1: Calculate the volume of the plastic block.
\[
\text{Volume} = \text{length} \times \text{width} \times \text{height}
\]
\[
\text{Volume} = 2 \, \text{cm} \times 4 \, \text{cm} \times 5 \, \text{cm} = 40 \, \text{cm}^3
\]

#### Step 2: Use the density formula to find the mass.
\[
\text{Mass} = \text{Density} \times \text{Volume}
\]
\[
\text{Mass} = 2 \, \text{g/cm}^3 \times 40 \, \text{cm}^3 = 80 \, \text{g}
\]

#### Final Answer:
\[
\boxed{80 \, \text{g}}
\]

---

Problem 2:

The density of a piece of metal is \(8 \, \text{g/cm}^3\) and its volume is \(100 \, \text{cm}^3\). What is the mass of the sample of metal?

#### Step 1: Use the density formula to find the mass.
\[
\text{Mass} = \text{Density} \times \text{Volume}
\]
\[
\text{Mass} = 8 \, \text{g/cm}^3 \times 100 \, \text{cm}^3 = 800 \, \text{g}
\]

#### Final Answer:
\[
\boxed{800 \, \text{g}}
\]

---

Problem 3:

Find the mass of an object with a volume of \(2 \, \text{cm}^3\) and a density of \(3.5 \, \text{g/cm}^3\).

#### Step 1: Use the density formula to find the mass.
\[
\text{Mass} = \text{Density} \times \text{Volume}
\]
\[
\text{Mass} = 3.5 \, \text{g/cm}^3 \times 2 \, \text{cm}^3 = 7 \, \text{g}
\]

#### Final Answer:
\[
\boxed{7 \, \text{g}}
\]

---

Problem 4:

What is the volume of an object with a density of \(2 \, \text{g/cm}^3\) and a mass of \(40 \, \text{g}\)?

#### Step 1: Rearrange the density formula to solve for volume.
\[
\text{Volume} = \frac{\text{Mass}}{\text{Density}}
\]
\[
\text{Volume} = \frac{40 \, \text{g}}{2 \, \text{g/cm}^3} = 20 \, \text{cm}^3
\]

#### Final Answer:
\[
\boxed{20 \, \text{cm}^3}
\]

---

Problem 5:

If the mass of an object is \(27 \, \text{g}\) and its density is \(9 \, \text{g/cm}^3\), what is the volume of the object?

#### Step 1: Rearrange the density formula to solve for volume.
\[
\text{Volume} = \frac{\text{Mass}}{\text{Density}}
\]
\[
\text{Volume} = \frac{27 \, \text{g}}{9 \, \text{g/cm}^3} = 3 \, \text{cm}^3
\]

#### Final Answer:
\[
\boxed{3 \, \text{cm}^3}
\]

---

Problem 6:

The density of a liquid is \(3 \, \text{g/cm}^3\) and its mass is \(30 \, \text{g}\). What is the volume of the liquid?

#### Step 1: Rearrange the density formula to solve for volume.
\[
\text{Volume} = \frac{\text{Mass}}{\text{Density}}
\]
\[
\text{Volume} = \frac{30 \, \text{g}}{3 \, \text{g/cm}^3} = 10 \, \text{cm}^3
\]

#### Final Answer:
\[
\boxed{10 \, \text{cm}^3}
\]

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Final Answers:

1. \(\boxed{80 \, \text{g}}\)
2. \(\boxed{800 \, \text{g}}\)
3. \(\boxed{7 \, \text{g}}\)
4. \(\boxed{20 \, \text{cm}^3}\)
5. \(\boxed{3 \, \text{cm}^3}\)
6. \(\boxed{10 \, \text{cm}^3}\)