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 smallest volume? a aluminum, mass = 138 g, d = 2.7 g/cm³ b copper, mass = 225 g, d = 8.92 g/cm³ c iron, mass = 235 g, d = 7.86 g/cm³ d magnesium, mass = 105 g, d = 1.74 g/cm³ e silver, mass = 215 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 $V = \frac{m}{
ho}$.

Step2: Calculate volume of aluminum

For aluminum, $m = 138$ g and $
ho=2.7$ g/cm³. So $V_{Al}=\frac{138}{2.7}\approx51.11$ cm³.

Step3: Calculate volume of copper

For copper, $m = 225$ g and $
ho = 8.92$ g/cm³. So $V_{Cu}=\frac{225}{8.92}\approx25.22$ cm³.

Step4: Calculate volume of iron

For iron, $m = 235$ g and $
ho = 7.86$ g/cm³. So $V_{Fe}=\frac{235}{7.86}\approx29.90$ cm³.

Step5: Calculate volume of magnesium

For magnesium, $m = 105$ g and $
ho = 1.74$ g/cm³. So $V_{Mg}=\frac{105}{1.74}\approx60.34$ cm³.

Step6: Calculate volume of silver

For silver, $m = 215$ g and $
ho = 10.5$ g/cm³. So $V_{Ag}=\frac{215}{10.5}\approx20.48$ cm³.

Step7: Compare volumes

Comparing $V_{Al}\approx51.11$ cm³, $V_{Cu}\approx25.22$ cm³, $V_{Fe}\approx29.90$ cm³, $V_{Mg}\approx60.34$ cm³ and $V_{Ag}\approx20.48$ cm³, we can see that silver has the smallest volume.

Answer:

E. silver, mass = 215 g, d = 10.5 g/cm³