Posted by **annie** on Wednesday, March 27, 2013 at 11:42am.

An open box is made from a rectangular piece of cardboard measuring 16 cm by 10cm. Four equal squares are to be cut from each corner and flaps folded up.

Find the length of the side of the square which makes the volume of the box as large as possible.

Find the largest volume

- math -
**Steve**, Wednesday, March 27, 2013 at 11:50am
the base of the box is 16-2x by 10-2x, and the height is x

v = x(16-2x)(10-2x)

v'= 4(x-2)(3x-20)

20/3 >5, so it's too large

so, max volume occurs when x=2

The box is 6x12x2 with volume 144

- math -
**annie**, Wednesday, March 27, 2013 at 11:58am
@steve

Why is the base of the box 16-2x by 10-2x

(where did the 2x come from?)

- math -
**Steve**, Wednesday, March 27, 2013 at 12:17pm
because x was cut off each corner. Draw a diagram, and you will see that when the corners are turned up, the sides have 2x cut off.

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