Q. 385.0( 1 Vote )

Answer :

Let L be the length of the square base and h be the height/depth of the tank.

Expenses of lining implies the cost for lining the entire inner surface area of the tank; a base and four vertical sides.

If we have minimum area to cover, we will have minimum costs incurred.

Internal area of the tank = L^{2} + 4Lh

Volume of the tank = L^{2}h = V

Therefore,

We get two outcomes here.

L = 0,2h

We discard L = 0, as it makes no sense.

So;

L = 2h.

Now to check whether a maxima or a minima exists

Therefore a minima exists for all non zero values of L.

Hence for the tank lining costs to be minimum, h = L/2.

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