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?

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Answer 1 · 2017-12-20T11:37:39

Approx. #6*cm^3#...that's a big sparkler....and I think this is the famous #"Kohi-noor"#, the one that presently lies in QE11's crown.....

By definition #rho_"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?

Answer 2 · 2017-12-20T11:47:46

#5.97 cm^3#

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

Rearrange for volume:
#Volume (cm^3) = (Mass (g)) / (Density (gcm^(-3)))#

#Volume = (21 g) / (3.52 gcm^(-3))#

#Volume = 5.97 cm^3#

A note on units
#cm^3# is another way of writing #mL#
#gcm^(-3)# is another way of writing #g#/#cm^3#