To determine the correct volume of the sample using the provided formula and values:

Given:

• Density, $D = 2.00 \, \text{g/cm}^3$
• Mass, $m = 0.5 \, \text{g}$
• Formula for density: $D = \frac{m}{V}$

We need to determine the volume, $V$, by rearranging the formula: $V = \frac{m}{D}$

Substitution:

$V = \frac{0.5}{2.00}$

Calculation:

$V = 0.25 \, \text{cm}^3$

Conclusion:

The correct answer is Option A: "The volume is $0.25 \, \text{cm}^3$ because $V = \frac{m}{D}$."

Would you like me to explain any steps further or solve another related question?

Here are 5 related questions to expand on this:

1. What is the density if the mass is 6 g and the volume is 3 cm³?
2. Rearrange the formula $D = \frac{m}{V}$ to solve for mass ($m$).
3. If a mineral has a density of 5 g/cm³ and a volume of 2 cm³, what is its mass?
4. What happens to the volume if the density is doubled but the mass stays the same?
5. How does the formula for density relate to the concepts of mass and volume?

Tip:

Always check units in calculations involving density, mass, and volume to ensure consistency and accuracy!