Answer :
The volume of the metal with a mass of 21.2 grams is approximately 0.0 cubic centimeters.
How to determine the volume, in cubic centimeters, of a piece of metal that has a mass of 21, point, 2, 321.23 grams.
To find the volume of a piece of metal with a mass of 21.2 grams, you can use the given data points to create a mass-volume relationship. Then, use this relationship to determine the volume.
Let's create a linear relationship between mass and volume based on the data:
Data Point 1: Mass = 9.9 grams, Volume = 10.6 cubic centimeters
Data Point 2: Mass = 10.6 grams, Volume = 10.2 cubic centimeters
Data Point 3: Mass = 13.1 grams, Volume = 12.4 cubic centimeters
Now, you can calculate the slope (rate of change) of the relationship:
Slope = (Change in Volume) / (Change in Mass)
Slope = [(10.2 - 10.6) cm³] / [(10.6 - 9.9) g]
Slope = (-0.4 cm³) / (0.7 g)
Now that you have the slope, you can use it to find the volume for a mass of 21.2 grams:
Volume = (Slope) * (Mass) + (Volume at Data Point 2)
Volume = (-0.4/0.7 cm³/g) * 21.2 g + 10.2 cm³
Now, calculate the volume:
Volume = (-0.5714 cm³/g) * 21.2 g + 10.2 cm³
Volume ≈ -12.13 cm³ + 10.2 cm³
Since volume cannot be negative, the negative portion indicates that the mass given is not within the range of the data points. Therefore, the volume should be zero.
So, the volume of the metal with a mass of 21.2 grams is approximately 0.0 cubic centimeters.
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