Question

The block of aluminum shown above has a height of 4.0mm, a width of 6.0mm, and a depth of 1.8mm. If its mass is 116.64 mg, what is its density in g/cm³? (Give answer in 2 significant figures)

Answer 1

The density of the aluminum block is calculated by converting the mass from milligrams to grams and multiplying the dimensions to get the volume in cubic centimeters. Then, the density formula (p = m/V) is used, resulting in a density of 2.7 g/cm³, which should be reported in two significant figures.

Step-by-step explanation:

The student's question is concerning the calculation of the density of a block of aluminum given its dimensions and mass. To find the density, which is the mass-to-volume ratio, we use the formula p = m/V, where p is density, m is mass, and V is volume.

First, we need to convert the measurements into consistent units. The mass is given in milligrams (mg) and dimensions in millimeters (mm). We convert 116.64 mg to grams (0.11664 g), and the dimensions to cubic centimeters (cm³). The volume of the block of aluminum in cm³ is calculated by multiplying its height (0.4 cm), width (0.6 cm), and depth (0.18 cm), giving 0.0432 cm³.

Now, we can calculate the density:
p = m/V = 0.11664 g / 0.0432 cm³ = 2.7 g/cm³

Thus, the density of the aluminum block is approximately 2.7 g/cm³, which matches the experimentally known density of aluminum. However, it's important to note that the answer should be reported in two significant figures as requested by the student, which would be 2.7 g/cm³.