Mass, Volume, and Density Practice Problems & Review Worksheet with solutions.

Problem Analysis and Solution Explanation

The provided worksheet focuses on the concepts of mass, volume, and density. The problems require calculations and understanding of the relationships between these quantities. Below, I will solve each problem step-by-step and explain the reasoning.

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#### Problem 1:
A metal ball has a mass of 2 kg and a volume of 6 cm³. What is its density?

- Formula: Density \( D = \frac{\text{Mass}}{\text{Volume}} \)
- Given:
- Mass \( m = 2 \, \text{kg} \)
- Volume \( V = 6 \, \text{cm}^3 \)
- Solution:
\[
D = \frac{m}{V} = \frac{2 \, \text{kg}}{6 \, \text{cm}^3} = 0.33 \, \text{kg/cm}^3
\]
- Answer: \( D = 0.33 \, \text{kg/cm}^3 \)

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#### Problem 2:
A certain gas expands to fill a 3 L container. Its mass is measured to be 0.6 kg. What is its density?

- Formula: Density \( D = \frac{\text{Mass}}{\text{Volume}} \)
- Given:
- Mass \( m = 0.6 \, \text{kg} \)
- Volume \( V = 3 \, \text{L} \)
- Solution:
\[
D = \frac{m}{V} = \frac{0.6 \, \text{kg}}{3 \, \text{L}} = 0.2 \, \text{kg/L}
\]
- Answer: \( D = 0.2 \, \text{kg/L} \)

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#### Problem 3:
A solid is 5 cm tall, 3 cm wide, and 2 cm thick. It has a mass of 129 g. What is its density?

- Formula: Density \( D = \frac{\text{Mass}}{\text{Volume}} \)
- Step 1: Calculate the volume of the solid.
\[
\text{Volume} = \text{Length} \times \text{Width} \times \text{Height} = 5 \, \text{cm} \times 3 \, \text{cm} \times 2 \, \text{cm} = 30 \, \text{cm}^3
\]
- Step 2: Use the density formula.
\[
D = \frac{m}{V} = \frac{129 \, \text{g}}{30 \, \text{cm}^3} = 4.3 \, \text{g/cm}^3
\]
- Answer: \( D = 4.3 \, \text{g/cm}^3 \)

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#### Problem 4:
What is the volume of a marble that has a mass of 3 g and a density of 2.7 g/cm³?

- Formula: Volume \( V = \frac{\text{Mass}}{\text{Density}} \)
- Given:
- Mass \( m = 3 \, \text{g} \)
- Density \( D = 2.7 \, \text{g/cm}^3 \)
- Solution:
\[
V = \frac{m}{D} = \frac{3 \, \text{g}}{2.7 \, \text{g/cm}^3} \approx 1.11 \, \text{cm}^3
\]
- Answer: \( V \approx 1.11 \, \text{cm}^3 \)

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#### Problem 5:
A graduated cylinder is filled to an initial volume of 12.7 mL. A rock is dropped into the graduated cylinder. The final volume of the graduated cylinder is 18.2 mL. What is the rock's volume in both mL and cm³? What method was used to determine this?

- Step 1: Calculate the volume of the rock using the water displacement method.
\[
\text{Volume of rock} = \text{Final volume} - \text{Initial volume} = 18.2 \, \text{mL} - 12.7 \, \text{mL} = 5.5 \, \text{mL}
\]
- Step 2: Convert mL to cm³ (since 1 mL = 1 cm³).
\[
\text{Volume of rock} = 5.5 \, \text{cm}^3
\]
- Method: Water displacement
- Answer: Volume of rock = \( 5.5 \, \text{mL} \) or \( 5.5 \, \text{cm}^3 \)

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#### Problem 6:
What is mass? What instrument is used to measure mass? What are the basic units of mass?

- Definition: Mass is the amount of matter in an object.
- Instrument: A triple beam balance is used to measure mass.
- Units: The basic units of mass are grams (g) and kilograms (kg).
- Answer:
- Mass: Amount of matter in an object.
- Instrument: Triple beam balance.
- Units: Grams (g) and kilograms (kg).

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#### Problem 7:
What is volume? What instrument is used to measure liquid volume? What formula is used to calculate the volume of a solid object?

- Definition: Volume is the amount of space occupied by an object.
- Instrument for liquid volume: A graduated cylinder is used to measure liquid volume.
- Formula for solid volume: For a rectangular solid, the volume is calculated as:
\[
V = \text{Length} \times \text{Width} \times \text{Height}
\]
- Answer:
- Volume: Amount of space occupied by an object.
- Instrument: Graduated cylinder.
- Formula: \( V = \text{L} \times \text{W} \times \text{H} \).

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#### Problem 8:
In terms of volume, how do mL and cm³ relate to one another?

- Relationship: 1 mL is equal to 1 cm³.
- Answer: They are equal. \( 1 \, \text{mL} = 1 \, \text{cm}^3 \).

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#### Problem 9:
What is density? What formula is used to calculate density?

- Definition: Density shows the relationship or ratio between the mass of an object and its volume.
- Formula: Density \( D = \frac{\text{Mass}}{\text{Volume}} \)
- Answer:
- Density: Relationship between mass and volume.
- Formula: \( D = \frac{M}{V} \).

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Final Answer:

\[
\boxed{
\begin{aligned}
1. & \, D = 0.33 \, \text{kg/cm}^3 \\
2. & \, D = 0.2 \, \text{kg/L} \\
3. & \, D = 4.3 \, \text{g/cm}^3 \\
4. & \, V \approx 1.11 \, \text{cm}^3 \\
5. & \, \text{Volume of rock} = 5.5 \, \text{mL} \, \text{or} \, 5.5 \, \text{cm}^3 \\
6. & \, \text{Mass: Amount of matter; Instrument: Triple beam balance; Units: g, kg} \\
7. & \, \text{Volume: Space occupied; Instrument: Graduated cylinder; Formula: } V = \text{L} \times \text{W} \times \text{H} \\
8. & \, 1 \, \text{mL} = 1 \, \text{cm}^3 \\
9. & \, \text{Density: Mass/Volume; Formula: } D = \frac{M}{V}
\end{aligned}
}
\]