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September 15, 2014

September 15, 2014

Posted by **anu** on Friday, January 7, 2011 at 1:36am.

- calculus -
**Reiny**, Friday, January 7, 2011 at 9:02amI will assume that by "most economical" you mean

"minimum cost of material for surface area".

let each side of the end square be x, so the radius for the end circles is also x

let the height be y

SA = 2x^2 + 2πxh

but V = 400

400 = πr^2h

h = 400/(πr^2)

SA = 2x^2 + 2πx(400/(πx^2)

= 2x^2 + 800/x

find d(SA)/dx

set it equal to zero and solve for x

straightforward from here.

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