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January 31, 2015

January 31, 2015

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

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 11:50amthe 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 12:17pmbecause 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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