Question

The density of diamond is 3.51 g/cm3 . the international (but non-si) unit for weighing diamonds is the "carat" (1 carat = 200 mg exactly.) what is volume of a 0.87 carat diamond? answer in units of cm3 .

Answer 1

To calculate the volume of the diamond, we use the formula

$\rho =\frac{m}{V}$

Here, $\rho$ is the density and its value given $3.51 g/cm^3$

and m is mass and its value given$0.87 carat$.

1 carat = 200 mg = 0.200 g

So mass of the diamond, $m= 0.87 carat \times 0.200 g/carat = 0.174 g$

Substituting these values in above equation we get,

$\rho =\frac{0.174 g}{3.51 g/cm^3} =0.0495 cm^3$

Thus the volume of given carat diamond is $0.0495 cm^3$.