From the information given,
density of ice = 880 kg/m^3
Let the height of the cube be h meters.
All sides of a cube are equal.
Volume of cube = s^3
where s is the length of each side. Thus,
Volume of this cube = h^3
If 92% is submerged, then
height submerged = 92/100 x h = 92h/100
Also, let the density of the drink be Po
Buoyancy force acting on ice cube = Po x volume of ice submerged x g Recall,
mass = density x volume
Force = mg
where
m is mass
g is acceleration due to gravity
Thus,
Buoyancy force on ice cube = Po x h^2 x 92h/100 x g
Force acting on ice cube = density of ice x volume of ice x g
Force acting on ice cube = 880 x h^3 x g
If ice is floating,
then buoyancy force = gravitational force
Thus,
Po x h^2 x 92h/100 x g = 880 x h^3 x g
h^3 cancels out on both sides
g cancels out too. It becomes
92Po/100 = 880
0.92Po = 880
Po = 880/0,92
Po = 956.5 kg/m^3
The density of the drink you mixed is 956.5 kg/m^3
