To determine which metal most likely matches the composition of the meteorite, we need to calculate the density of the meteorite and then compare it with the given densities of aluminum, iron, and lead.
Here are the steps to perform this calculation:
1. Calculate the density of the meteorite:
- The formula to calculate density is:
[tex]\[
\text{Density} = \frac{\text{Mass}}{\text{Volume}}
\][/tex]
- Given:
- Mass of the meteorite: [tex]\( 370 \, g \)[/tex]
- Volume of the meteorite: [tex]\( 50 \, cm^3 \)[/tex]
- Substitute the values into the formula:
[tex]\[
\text{Density of meteorite} = \frac{370 \, g}{50 \, cm^3} = 7.4 \, g/cm^3
\][/tex]
2. Compare the calculated density with the given densities of the metals:
- Density of aluminum: [tex]\( 2.64 \, g/cm^3 \)[/tex]
- Density of iron: [tex]\( 7.50 \, g/cm^3 \)[/tex]
- Density of lead: [tex]\( 11.34 \, g/cm^3 \)[/tex]
3. Determine the likely metal:
- The density of the meteorite is [tex]\( 7.4 \, g/cm^3 \)[/tex].
- Compare [tex]\( 7.4 \, g/cm^3 \)[/tex] with each given density:
- [tex]\( 7.4 \, g/cm^3 \)[/tex] does not match [tex]\( 2.64 \, g/cm^3 \)[/tex] (aluminum).
- [tex]\( 7.4 \, g/cm^3 \)[/tex] does not match [tex]\( 7.50 \, g/cm^3 \)[/tex] (iron).
- [tex]\( 7.4 \, g/cm^3 \)[/tex] does not match [tex]\( 11.34 \, g/cm^3 \)[/tex] (lead).
Since the density of [tex]\( 7.4 \, g/cm^3 \)[/tex] does not exactly match the density of aluminum, iron, or lead, we conclude that the meteorite's composition does not correspond to any of these metals.
Therefore, the most likely answer is:
none of these (density is less than 1.0)
