Math Problem Statement
A straightforward method of finding the density of an object is to measure its mass and then measure its volume by submerging it in a graduated cylinder. What is the density (in g/cm3) of a 240 g rock that displaces 87.0 cm3 of water? (Note that the accuracy and practical applications of this technique are more limited than a variety of others that are based on Archimedes' principle.)
Solution
To find the density of the rock, we use the formula:
Given:
- Mass of the rock,
- Volume of the rock, (based on water displacement)
Plugging in the values:
Answer: The density of the rock is approximately .
Would you like more details or have any questions?
Here are 5 related questions to further explore the topic:
- How would the density calculation change if the rock displaced 90 cm³ of water?
- What are some limitations of using water displacement to measure volume, especially for porous objects?
- How does Archimedes' principle relate to measuring the density of irregularly shaped objects?
- Can you find the density if only the weight in newtons and volume in liters are provided?
- How would temperature variations affect the density of the water and, consequently, the density calculation?
Tip: When using water displacement, ensure there are no air bubbles on the submerged object, as they can affect the volume reading.
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Math Problem Analysis
Mathematical Concepts
Density
Volume
Mass
Archimedes' Principle
Formulas
Density = Mass / Volume
Theorems
Archimedes' Principle
Suitable Grade Level
Grades 7-9
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