To calculate the volume of the diamond, we use the formula
[tex]\rho =\frac{m}{V}[/tex]
Here, [tex]\rho[/tex] is the density and its value given [tex]3.51 g/cm^3[/tex]
and m is mass and its value given[tex]0.87 carat[/tex].
1 carat = 200 mg = 0.200 g
So mass of the diamond, [tex]m= 0.87 carat \times 0.200 g/carat = 0.174 g[/tex]
Substituting these values in above equation we get,
[tex]\rho =\frac{0.174 g}{3.51 g/cm^3} =0.0495 cm^3[/tex]
Thus the volume of given carat diamond is [tex]0.0495 cm^3[/tex].
