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April 1, 2015

April 1, 2015

Posted by **irma** on Sunday, May 12, 2013 at 1:38am.

- math -
**Reiny**, Sunday, May 12, 2013 at 6:43amlet the size of the cut-out square be x cm by x cm

then after bending,

the base of the box will be 30-2x by 30-2x and x cm high

Volume = x(30-2x)^2

= x(900 - 120x + 4x^2)

= 4x^3 - 120x^2 + 900x

d(Volume)/dx = 12x^2 - 240x + 900

= 0 for a max/min of Volume

12x^2 - 240x + 900 = 0

x^2 - 20x + 75 = 0

(x-5)(x-15) = 0

x = 5 or x = 15 , (clearly x = 15 yields a minimum volume of 0)

So the size of the cut should be squares of 5 cm by 5 cm.

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