To figure out which material or object is the most dense based on its mass and volume, you use the formula for density:
\[ \text{Density} (\rho) = \frac{\text{Mass} (m)}{\text{Volume} (V)} \]
Where:
- \(\rho\) is the density,
- \(m\) is the mass,
- \(V\) is the volume.
Here are the steps to calculate and identify the material with the highest density:
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Measure Mass and Volume: Obtain the mass and volume of each material or object you are comparing. Make sure the measurements are in consistent units (e.g., grams and cubic centimeters, or kilograms and cubic meters).
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Calculate Density: For each material or object, divide the mass by the volume to get the density:
\[ \rho = \frac{m}{V} \]
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Compare Densities: Once you have the density calculated for each material, compare the values. The material or object with the highest density value is the most dense.
Example
Let’s say you have two materials with the following properties:
- Material A: Mass = 200 grams, Volume = 100 cubic centimeters
- Material B: Mass = 300 grams, Volume = 150 cubic centimeters
Calculating Density:
For Material A: \[ \rho_A = \frac{200 \text{ g}}{100 \text{ cm}^3} = 2 \text{ g/cm}^3 \]
For Material B: \[ \rho_B = \frac{300 \text{ g}}{150 \text{ cm}^3} = 2 \text{ g/cm}^3 \]
In this example, both materials have the same density of \(2 \text{ g/cm}^3\).
If you had another Material C with a mass of 500 grams and a volume of 100 cubic centimeters:
For Material C: \[ \rho_C = \frac{500 \text{ g}}{100 \text{ cm}^3} = 5 \text{ g/cm}^3 \]
Now, comparing all three:
- Material A: \(2 \text{ g/cm}^3\)
- Material B: \(2 \text{ g/cm}^3\)
- Material C: \(5 \text{ g/cm}^3\)
Material C is the most dense.
Summary
To find the most dense material, you calculate the density using the formula \(\rho = \frac{m}{V}\) for each material, then compare the densities to determine which one is the highest.