What volume of the piece of the quartz will be submerged when floating in a container of mercury?

Question

A piece of quartz (d=2.65 g/cm^3) has a volume of 10 cm^3. What volume of the piece of the quartx will be submerged when floating in a container of mercury (d=13.6 g/cm^3).

Answer 1

The cube weighs 26.5 gm
It will sink until this weight of mercury is displaced.
26.5 / 13.6 = 1.94852941 cm3

Answer 2

Mass of quartz = 10 x 2.65 gm

Mass of mercury displaced by quartz

= 13.6 V (V is the volume of quartz submerged in mercury)

13.6 V = 10 x 2.65 gm

V = 10 x 2.65 /13.6 = 1.95 (cm)^3.

Answer 3

Logic seems to say it will float completely, but maybe not.