Math Is Fun Forum

niharika_kumar

Member

From: Numeraland

Registered: 2013-02-12

Posts: 1,062

an open tank

A sheet of area 40 m^2 is used to make an open tank with a square base. Find the dimensions of the base such that volume of this tank is minimum.

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Agnishom

Real Member

From: Riemann Sphere

Registered: 2011-01-29

Posts: 24,996

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Re: an open tank

I think the base should be a square of area 8 m^2

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'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
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Bob

Administrator

Registered: 2010-06-20

Posts: 10,626

Re: an open tank

hi Niharika,

???  If you make the base a square with side = root(40) then there is no area left to make any sides, so the volume is zero.  I cannot get any lower than that!

Are you sure you want minimum and not maximum ?

And one more thing.  An open top tank with side of base = x will have surface area = x^2 + 4xh, where h is the height of the sides.  If all of the 40 is used up with no wastage then

so

Then you can differentiate to find the stationary points and identify the minimum(maximum).

But to turn a flat sheet into an open box, you can cut a square h x h from each corner, and then fold up the sides.  The method is essentially the same but the algebra is more complicated and will lead to a different function.  I wonder if this is what is required.  ???

Bob

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