To calculate the density of magnesium metal, we will follow the steps below:
1. Identify the given values:
- The volume of the magnesium block is [tex]\(460 \, \text{cm}^3\)[/tex].
- The mass of the magnesium block is [tex]\(1.51 \times 10^3 \, \text{g}\)[/tex].
2. Write the formula for density:
[tex]\[
\text{Density} (\rho) = \frac{\text{Mass}}{\text{Volume}}
\][/tex]
3. Substitute the given values into the density formula:
[tex]\[
\text{Density} = \frac{1.51 \times 10^3 \, \text{g}}{460 \, \text{cm}^3}
\][/tex]
4. Perform the division:
[tex]\[
\text{Density} = \frac{1510 \, \text{g}}{460 \, \text{cm}^3} \approx 3.2826 \, \text{g/cm}^3
\][/tex]
5. Express the answer with the correct number of significant figures:
- The volume [tex]\(460 \, \text{cm}^3\)[/tex] has three significant figures.
- The mass [tex]\(1.51 \times 10^3 \, \text{g}\)[/tex] has three significant figures.
- Therefore, our final answer should be expressed with three significant figures.
The density of magnesium metal is:
[tex]\[
\boxed{3.28 \, \text{g/cm}^3}
\][/tex]
So the correct answer is [tex]\(3.28 \, \text{g/cm}^3\)[/tex].
