Question

you have a sample of each of the following five metals, with the mass and density of each sample given. which sample has the largest volume? answer: a aluminum, mass = 135 g, d = 2.7 g/cm³ b copper, mass = 305 g, d = 8.92 g/cm³ c iron, mass = 240 g, d = 7.87 g/cm³ d magnesium, mass = 75 g, d = 1.74 g/cm³ e silver, mass = 420 g, d = 10.5 g/cm³

Explanation:

Step1: Recall density formula

The density formula is $
ho=\frac{m}{V}$, where $
ho$ is density, $m$ is mass and $V$ is volume. We can re - arrange it to find volume $V = \frac{m}{
ho}$.

Step2: Calculate volume of aluminum

For aluminum, $m = 135\ g$ and $
ho=2.7\ g/cm^{3}$. So $V_{Al}=\frac{135}{2.7}=50\ cm^{3}$.

Step3: Calculate volume of copper

For copper, $m = 305\ g$ and $
ho = 8.92\ g/cm^{3}$. So $V_{Cu}=\frac{305}{8.92}\approx34.2\ cm^{3}$.

Step4: Calculate volume of iron

For iron, $m = 240\ g$ and $
ho = 7.87\ g/cm^{3}$. So $V_{Fe}=\frac{240}{7.87}\approx30.5\ cm^{3}$.

Step5: Calculate volume of magnesium

For magnesium, $m = 75\ g$ and $
ho = 1.74\ g/cm^{3}$. So $V_{Mg}=\frac{75}{1.74}\approx43.1\ cm^{3}$.

Step6: Calculate volume of silver

For silver, $m = 420\ g$ and $
ho = 10.5\ g/cm^{3}$. So $V_{Ag}=\frac{420}{10.5}=40\ cm^{3}$.

Step7: Compare volumes

Comparing $V_{Al}=50\ cm^{3}$, $V_{Cu}\approx34.2\ cm^{3}$, $V_{Fe}\approx30.5\ cm^{3}$, $V_{Mg}\approx43.1\ cm^{3}$, $V_{Ag}=40\ cm^{3}$, we can see that aluminum has the largest volume.

Answer:

A. aluminum, mass = 135 g, d = 2.7 g/cm³