A small statue has a mass of 723.4g and displaces 68.6mL of water when added to a container of water.

Question

a.) What is the density of the solid used to make the statue?

b.) You need to determine the density of a solid cube. Although you could determine the cube's density the same way the density of the statue was determined, describe an alternative method you could use?

Answer 1

Hi Paula,

(a) For this part, the volume of water (V_w) displaced by the statue is equal to the volume of the statue (V), according to Archimedes’ principle.
M = 723.4 g,
V_w= 68.6 mL =68.6 cm³
This is also the volume of the statue
V = V_w
ρ = M/V =723.4 g/68.6 cm³
   =10.545g/cm³

(b) If you need to determine the density of a cube in another way, place it in a fluid of known density (ρ_fuid). The volume of cube submerged(V_submerged) is equal to volume of fluid displaced, since the volume of the cube is known (V_cube), the fraction of the cube that is submerged give is equal to the specific gravity of the cube (the ratio of the density of the cube to that of the fluid)

 ρ_cube  = (V_submerged/V_cube)ρ_fluid