Here are the step-by-step solutions for each problem on the worksheet.
1) Brown Sugar Density
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Formula: Density = Mass ÷ Volume
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Given: Mass = 12.9 g, Volume = 8 cm³
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Calculation: $12.9 \div 8 = 1.6125$
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Rounding: We round to two decimal places.
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Answer: 1.61 g/cm³
2) Cooking Oil Density
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Formula: Density = Mass ÷ Volume
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Given: Mass = 43.5 g, Volume = 50 mL
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Calculation: $43.5 \div 50 = 0.87$
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Answer: 0.87 g/mL
3) Mass of a Liquid
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Formula: Mass = Density × Volume
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Given: Density = 2.5 g/mL, Volume = 15 mL
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Calculation: $2.5 \times 15 = 37.5$
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Answer: 37.5 g
4) Volume of a Liquid
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Formula: Volume = Mass ÷ Density
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Given: Mass = 65 g, Density = 5.45 g/mL
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Calculation: $65 \div 5.45 \approx 11.9266...$
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Rounding: Round to two decimal places.
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Answer: 11.93 mL
5) Aluminum Cube Density
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Step 1: Find Volume. Since it is a cube, Volume = side × side × side.
* $4 \text{ cm} \times 4 \text{ cm} \times 4 \text{ cm} = 64 \text{ cm}^3$
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Step 2: Find Density. Density = Mass ÷ Volume.
* $176 \text{ g} \div 64 \text{ cm}^3 = 2.75$
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Answer: 2.75 g/cm³
6) Cork Density
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Note: When an object displaces water, the amount of water displaced equals the volume of the object. So, Volume = 23.5 mL.
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Formula: Density = Mass ÷ Volume
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Given: Mass = 5.7 g, Volume = 23.5 mL
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Calculation: $5.7 \div 23.5 \approx 0.2425...$
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Rounding: Round to two decimal places.
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Answer: 0.24 g/mL
7) Granite Block Density
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Step 1: Find Volume. Volume = Length × Width × Height.
* $20 \text{ cm} \times 5 \text{ cm} \times 10 \text{ cm} = 1000 \text{ cm}^3$
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Step 2: Find Density. Density = Mass ÷ Volume.
* $2700 \text{ g} \div 1000 \text{ cm}^3 = 2.7$
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Answer: 2.7 g/cm³
8) PVC Pipe Density
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Note: The displaced water tells us the volume of the pipe. Volume = 60 mL.
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Formula: Density = Mass ÷ Volume
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Given: Mass = 78 g, Volume = 60 mL
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Calculation: $78 \div 60 = 1.3$
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Answer: 1.3 g/mL
9) Magnesium Flare Density
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Formula: Density = Mass ÷ Volume
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Given: Mass = 1300 g, Volume = 743 cm³
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Calculation: $1300 \div 743 \approx 1.7496...$
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Rounding: Round to two decimal places.
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Answer: 1.75 g/cm³
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Final Answer:
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
Parent Tip: Review the logic above to help your child master the concept of density calculations worksheet.
