# Diamonds have a density of 3.52 g/mL. What is the volume (in units of cm3) of a diamond with a mass of 21 g?

Dec 20, 2017

Approx. $6 \cdot c {m}^{3}$...that's a big sparkler....and I think this is the famous $\text{Kohi-noor}$, the one that presently lies in QE11's crown.....

#### Explanation:

By definition ${\rho}_{\text{density"="mass"/"volume}}$

And thus if we want volume we take the quotient....

"volume"="mass"/rho=(21*g)/(3.52*g*mL^-1)=??*mL...is this quotient dimensionally consistent? Why?

Dec 20, 2017

$5.97 c {m}^{3}$

#### Explanation:

Using the equation:
Density (gcm^(-3)) = (Mass (g)) / (Volume (cm^3)

Rearrange for volume:
$V o l u m e \left(c {m}^{3}\right) = \frac{M a s s \left(g\right)}{D e n s i t y \left(g c {m}^{- 3}\right)}$

$V o l u m e = \frac{21 g}{3.52 g c {m}^{- 3}}$

$V o l u m e = 5.97 c {m}^{3}$

A note on units
$c {m}^{3}$ is another way of writing $m L$
$g c {m}^{- 3}$ is another way of writing $g$/$c {m}^{3}$