Figure shows a uniform metal ball suspended by thread of negligible mass from an upright cylinder that floats partially submerged in water. The cylinder has height 6 cm, face area 11 cm2 on the top and bottom and density 0.5 g/`cm^3`. 4 cm of cylinder’s height is inside the water surface. Density of the metal ball is 8gm/`cm^3`. R is the radius of the ball. It is found that `R^(3)-3/(alpha) cm^(3)` where `alpha` is an integer. Find `alpha.(rho_(w)=1 gm//cm^(3))` (system is in equilibrium)