density calculations worksheet with answers

Lemon

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04-02-2025

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This worksheet provides a comprehensive guide to density calculations, perfect for students learning about this fundamental concept in science. Each problem includes a step-by-step solution to help you understand the process. Remember, density (ρ) is calculated as mass (m) divided by volume (V): ρ = m/V. The units for density are typically g/cm³ or kg/m³.

Section 1: Basic Density Calculations

Instructions: Calculate the density for each of the following objects. Show your work and include units.

Problem 1: A block of wood has a mass of 150 grams and a volume of 200 cm³.

Solution:

1. Identify the givens: Mass (m) = 150 g; Volume (V) = 200 cm³
2. Apply the formula: ρ = m/V
3. Calculate: ρ = 150 g / 200 cm³ = 0.75 g/cm³
4. Answer: The density of the wood is 0.75 g/cm³.

Problem 2: A metal sphere has a mass of 500 kg and a volume of 0.1 m³.

Solution:

1. Identify the givens: Mass (m) = 500 kg; Volume (V) = 0.1 m³
2. Apply the formula: ρ = m/V
3. Calculate: ρ = 500 kg / 0.1 m³ = 5000 kg/m³
4. Answer: The density of the metal sphere is 5000 kg/m³.

Problem 3: A liquid sample has a mass of 25 grams and occupies a volume of 30 mL. (Remember, 1 mL = 1 cm³)

Solution:

1. Identify the givens: Mass (m) = 25 g; Volume (V) = 30 mL = 30 cm³
2. Apply the formula: ρ = m/V
3. Calculate: ρ = 25 g / 30 cm³ ≈ 0.83 g/cm³
4. Answer: The density of the liquid sample is approximately 0.83 g/cm³.

Section 2: Calculating Mass or Volume using Density

Instructions: Solve the following problems. Show your work and include units.

Problem 4: A substance with a density of 2.7 g/cm³ has a volume of 10 cm³. What is its mass?

Solution:

1. Identify the givens: Density (ρ) = 2.7 g/cm³; Volume (V) = 10 cm³
2. Rearrange the formula to solve for mass: m = ρ * V
3. Calculate: m = 2.7 g/cm³ * 10 cm³ = 27 g
4. Answer: The mass of the substance is 27 g.

Problem 5: A liquid with a density of 1.2 g/mL has a mass of 60 g. What is its volume?

Solution:

1. Identify the givens: Density (ρ) = 1.2 g/mL; Mass (m) = 60 g
2. Rearrange the formula to solve for volume: V = m/ρ
3. Calculate: V = 60 g / 1.2 g/mL = 50 mL
4. Answer: The volume of the liquid is 50 mL.

Section 3: Challenge Problem

Problem 6: A rectangular block of metal measures 5 cm x 10 cm x 2 cm. If its mass is 2000 g, what is its density?

Solution:

1. Calculate the volume: Volume (V) = length x width x height = 5 cm * 10 cm * 2 cm = 100 cm³
2. Identify the givens: Mass (m) = 2000 g; Volume (V) = 100 cm³
3. Apply the formula: ρ = m/V
4. Calculate: ρ = 2000 g / 100 cm³ = 20 g/cm³
5. Answer: The density of the metal block is 20 g/cm³.

This worksheet provides a solid foundation for understanding density calculations. Remember to always include units in your answers and to carefully check your work. Further practice with a variety of problems will solidify your understanding of this important concept.