# GATE2016-54

A vertical cylindrical tank with a flat roof and bottom is to be constructed for storing $150\:m^{3}$ of ethylene glycol. The cost of material and fabrication for the tank wall is Rs $6000$ per $m^{2}$ and the same for the roof and the tank bottom are Rs $2000$ and Rs $4000$ per $m^{2}$, respectively. The cost of accessories, piping and instruments can be taken as $10\%$ of the cost of the wall. $10\%$ of the volume of the tank needs to be kept free as vapour space above the liquid storage. What is the optimum diameter (in $m$) for the tank?
1. $3.5$
2. $3.9$
3. $7.5$
4. $7.8$