Calculating Density

Question

In determining the density of a rectangular metal bar, a chemist made the following measurements: length, 9.4 cm, width, 3.7 cm, height, 2.4 cm, mass, 45.9 g. Determine the density to the correct number of significant figures.

Answer 1

Start with the basic density formula:

Density = mass / volume

To find volume of a rectangular bar, multiply the length, width, and height:

volume = length x width x height

Combine the two formulas:

density = mass / (length x width x height)

Substitute the values:

density = 45.9 g / (9.4 cm x 3.7 cm x 2.4 cm)

Use your calculator to solve, keeping in mind that since the smallest # of significant digits in your givens is 2, your answer can only have 2:

0.55 g / cm^3

Answer 2

Density is mass per unit volume.

1. mass = 45.9 g
2. volume = L x W x H = 9.4 cm x 3.7 cm x 2.4 cm = 83.472 cm³
3. density = mass/volume = 45.9 g/83.472 cm³ = 0.54988 g/cm³
4. correct for significant figures: 0.55 cm³ since the sides of the cube are to only 2 significant figures