An aqueous solution feed of $1,000$ kg$/$h of $29$ wt$\%$ acetone is to be multistage countercurrent extracted with pure MIK to reduce the acetone concentration to $5\mathrm{.}0$ wt$\%$ in the final raffinate. Determine the number of theoretical stages necessary when using $2,500$ kg$/$h of solvent. Calculate diameter and height of the tower considering $50\%$ flooding speed, $60\%$ efficiency and Norton Intalox $3$T packaging.