A piece of gold leaf (density 19.3 g/cm3) weighs 1.93 mg. What is the volume in mm3?
The correct answer and explanation is :
To determine the volume of a piece of gold leaf, we use the formula:
[
\text{Volume} = \frac{\text{Mass}}{\text{Density}}
]
Step 1: Identify Given Values
- Density of gold = (19.3 \, \text{g/cm}^3)
- Mass of gold leaf = (1.93 \, \text{mg} = 0.00193 \, \text{g})
Step 2: Apply the Formula
[
\text{Volume} = \frac{0.00193 \, \text{g}}{19.3 \, \text{g/cm}^3}
]
[
\text{Volume} = 0.0001 \, \text{cm}^3
]
Step 3: Convert to mm³
Since (1 \, \text{cm}^3 = 1000 \, \text{mm}^3):
[
\text{Volume} = 0.0001 \times 1000 = 0.1 \, \text{mm}^3
]
Final Answer:
The volume of the gold leaf is (0.1 \, \text{mm}^3).
Explanation:
Gold is an extremely dense metal, meaning that even a very small amount of it occupies a tiny volume. The density of gold is 19.3 g/cm³, which means that 1 cm³ of gold weighs 19.3 grams. In this problem, we are given a mass of 1.93 mg, which is much smaller than a gram, so we expect a very small volume.
The key to solving this problem correctly is unit conversion. Since the mass is given in milligrams, we first convert it to grams because density is given in g/cm³. After dividing mass by density, we get the volume in cm³. Finally, we convert cm³ to mm³ because the problem specifically asks for mm³.
This problem highlights how density helps us determine volume from mass. Gold’s high density results in a very small volume for even a noticeable amount of mass. This is why gold can be beaten into extremely thin sheets—its mass remains substantial even when spread out over a large area.