Question

There is a proportional relationship between the mass and the volume of the pieces of metal. Determine the volume, in cubic centimeters, of a piece of metal that has a mass of 21.2, 321.23 grams. Round your answer to the nearest tenth.

a) 2,100.3 cm³
b) 1,050.2 cm³
c) 63.2 cm³
d) 2,132.5 cm³

Answer 1

To find the volume of a piece of metal given its mass, divide the mass by the metal's density. Using the density of aluminum (2.70 g/cm³), we can calculate that the volume for 21.2 grams is approximately 7.9 cm³ and for 321.23 grams, it's approximately 119.0 cm³. The options provided in the question do not match these results, indicating a possible error in the question.

Step-by-step explanation:

To determine the volume of a piece of metal with a mass of 21.2 grams and a mass of 321.23 grams, when there is a proportional relationship between mass and volume, we can use the concept of density, which is the mass-to-volume ratio. The density of aluminum, as given, is 2.70 g/cm³. Therefore, to find the volume for each mass, we can divide the mass by the density.

For the mass of 21.2 grams:

1. Volume = Mass / Density
2. Volume = 21.2 g / 2.70 g/cm³
3. Volume ≈ 7.9 cm³ (rounded to the nearest tenth)

For the mass of 321.23 grams:

1. Volume = Mass / Density
2. Volume = 321.23 g / 2.70 g/cm³
3. Volume ≈ 119.0 cm³ (rounded to the nearest tenth)

Both results are below the smallest volume option given (c) 63.2 cm³, which indicates there may be a misunderstanding. To solve for accurate volume measurements, we need to divide the given masses by the density of the specific metal in question, but it appears that the options listed are not consistent with the example given or a typo might have been made in the question statement.

Remember to keep track of your significant figures when performing calculations to ensure the correct level of precision in your answer.