Q. 38 5.0( 1 Vote )

An open tank is to be constructed with a square base and vertical sides so as to contain a given quantity of water. Show that the expenses of lining with lead will be least, if depth is made half of width.

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 = L2 + 4Lh

Volume of the tank = L2h = V


We get two outcomes here.

L = 0,2h

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


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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