math practice
on a separate sheet of paper, solve the following problems. show your work.
1. the mass of a liquid is $8.03 \times 10^4\text{ kg}$. the liquid fills up a $100,000\text{ l}$ tank. what is the density of this liquid?
2. you measure the mass of a piece of iron to be $17.37\text{ g}$ on an electronic balance. you then measure the volume to $2.21\text{ cm}^3$. what is the density of the iron?

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Accepted Answer

{ "quality": "clear", "question_count": 2, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Scientific Notation", "SI Units", "Unit Conversion" ], "new_concepts": [ "Density Calculation" ], "current_concepts": [ "Scientific Notation", "SI Units", "Unit Conversion", "Density Calculation" ] } ## Calculate density of the liquid in Question 1 $$ \begin{aligned} &m = 8.03 \times 10^4\text{ kg}\ &V = 100,000\text{ L} = 1.00 \times 10^5\text{ L}\ & ho = \frac{m}{V} = \frac{8.03 \times 10^4\text{ kg}}{1.00 \times 10^5\text{ L}} = 0.803\text{ kg/L} = 8.03 \times 10^{-1}\text{ kg/L} \end{aligned} $$ ## Calculate density of the iron in Question 2 $$ \begin{aligned} &m = 17.37\text{ g}\ &V = 2.21\text{ cm}^3\ & ho = \frac{m}{V} = \frac{17.37\text{ g}}{2.21\text{ cm}^3} \approx 7.8597\text{ g/cm}^3 \approx 7.86\text{ g/cm}^3 \end{aligned} $$ ## Question 1 $8.03 \times 10^{-1}\text{ kg/L}$ (or $0.803\text{ kg/L}$) ## Question 2 $7.86\text{ g/cm}^3$ { "subject": "Natural Science", "question_type": "Multi-part", "knowledge_point": [ "Natural Science", "Physics", "Density Calculation" ] }

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QUESTION IMAGE

Question

Explanation:

Calculate density of the liquid in Question 1

Calculate density of the iron in Question 2

Answer:

Question 1

Question 2