Silver has a density of 10.5 g/cm^3and gold has a density of 19.3 g/cm^3. Which would have a greater mass, 5 E\cm^3 of silver or 5 cm^3 of gold?

Sep 10, 2016

Clearly, the gold will have a greater mass, as it has a greater density.

Explanation:

$\text{Density}$ $=$ $\text{Mass"/"Volume}$

Thus $\text{Mass}$ $=$ $\text{Density"(rho)xx"volume}$

$\text{Mass of silver}$ $=$ $10.5 \cdot g \cdot \cancel{c {m}^{-} 3} \times 5 \cdot \cancel{c {m}^{3}}$ $=$ $52.5 \cdot g$.

$\text{Mass of gold}$ $=$ $19.3 \cdot g \cdot \cancel{c {m}^{-} 3} \times 5 \cdot \cancel{c {m}^{3}}$ $\cong$ $100 \cdot g$.

Note that I solved this problem dimensionally. I wanted an answer in grams; after cancelling out the units, I manifestly got an answer in grams. This is a check on whether I divided, multiplied, added correctly. It is all too easy to make an error.