A cylinder contains water to the extent of $\left (\displaystyle \frac{3}{4}\right)^{th}$ of its height. The radius and height of the cylinder are $14$ cm and $28$ cm respectively. Four solid metal sphere balls of radii $2$ cm, $4$ cm, $6$ cm and $8$ cm are dropped into the cylinder. What is the maximum raise in the height of the water level after the balls are dropped in it?