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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. $7.8$
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