density calculations worksheet answer key

Lemon

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02-02-2025

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This answer key provides solutions and detailed explanations for common density calculation problems. Understanding density is crucial in various scientific fields, from chemistry and physics to materials science and engineering. Remember that density (ρ) is defined as mass (m) per unit volume (V): ρ = m/V. The units commonly used are g/cm³ or kg/m³.

Section 1: Basic Density Calculations

Problem 1: A block of wood has a mass of 150 grams and a volume of 200 cubic centimeters. What is its density?

Answer:

• Step 1: Identify the given values: m = 150 g, V = 200 cm³
• Step 2: Apply the density formula: ρ = m/V = 150 g / 200 cm³ = 0.75 g/cm³

Therefore, the density of the wood is 0.75 g/cm³.

Problem 2: A metal sphere has a density of 8.9 g/cm³ and a volume of 5 cm³. What is its mass?

Answer:

• Step 1: Identify the given values: ρ = 8.9 g/cm³, V = 5 cm³
• Step 2: Rearrange the density formula to solve for mass: m = ρV = 8.9 g/cm³ * 5 cm³ = 44.5 g

Therefore, the mass of the metal sphere is 44.5 grams.

Problem 3: A liquid has a density of 1.2 g/mL and a mass of 36 grams. What is its volume?

Answer:

• Step 1: Identify the given values: ρ = 1.2 g/mL, m = 36 g
• Step 2: Rearrange the density formula to solve for volume: V = m/ρ = 36 g / 1.2 g/mL = 30 mL

Therefore, the volume of the liquid is 30 milliliters.

Section 2: More Complex Density Problems

Problem 4: A rectangular block of aluminum measures 10 cm x 5 cm x 2 cm. If the density of aluminum is 2.7 g/cm³, what is the mass of the block?

Answer:

• Step 1: Calculate the volume of the rectangular block: V = length x width x height = 10 cm * 5 cm * 2 cm = 100 cm³
• Step 2: Identify the density: ρ = 2.7 g/cm³
• Step 3: Calculate the mass using the density formula: m = ρV = 2.7 g/cm³ * 100 cm³ = 270 g

Therefore, the mass of the aluminum block is 270 grams.

Problem 5: An irregularly shaped object has a mass of 75 grams. When placed in a graduated cylinder containing 50 mL of water, the water level rises to 75 mL. What is the density of the object?

Answer:

• Step 1: Determine the volume of the object by subtracting the initial water level from the final water level: V = 75 mL - 50 mL = 25 mL
• Step 2: Identify the mass: m = 75 g
• Step 3: Calculate the density: ρ = m/V = 75 g / 25 mL = 3 g/mL

Therefore, the density of the irregularly shaped object is 3 g/mL.

Section 3: Unit Conversions

Problem 6: Convert a density of 1.5 g/cm³ to kg/m³.

Answer:

• Step 1: There are 100 cm in 1 meter, and 1000 grams in 1 kilogram. Therefore, (100 cm/m)³ = 1,000,000 cm³/m³ and (1 kg/1000 g).
• Step 2: Apply the conversion factors: 1.5 g/cm³ * (1 kg/1000 g) * (1,000,000 cm³/m³) = 1500 kg/m³

Therefore, the density is 1500 kg/m³.

This worksheet provides a solid foundation for understanding density calculations. Remember to always pay attention to units and ensure consistency throughout your calculations. Practice is key to mastering these concepts!