Question

The jewelers’ mass unit for a diamond is the carat. By definition, 1 carat equals exactly 200 mg. What is the volume of a 1.47 carat diamond? The density of diamond is 3.51 g/cm³. Answer in units of cm³.

A) 0.418 cm³
B) 0.529 cm³
C) 0.418 cm³
D) 0.529 cm³

Answer 1

The volume of a 1.47 carat diamond, using the density of diamond (3.51 g/cm³), is calculated to be 0.08376 cm³, which is approximately 0.084 cm³.

Step-by-step explanation:

To find the volume of a 1.47 carat diamond, we need to use the given density of diamond and the conversion of carats to milligrams.

First, convert carats to grams:

1. 1 carat = 200 milligrams.
2. 1.47 carats = 1.47 × 200 mg = 294 mg.
3. 294 mg = 0.294 grams (since 1 gram = 1000 milligrams).

Now, use the density formula, where density (d) = mass (m) / volume (v), and rearrange it to solve for volume:

v = m / d.

Using the density of diamond, 3.51 g/cm³:

v = 0.294 g / 3.51 g/cm³ = 0.08376 cm³.

The volume of the diamond is 0.08376 cm³, which can be rounded to 0.084 cm³ when considering significant figures based on the precision of the given data. Please note that the provided options do not contain the correct answer.