Cookies are packaged in boxes that measure 18cm by 20cm by 6cm. A larger box is being designed by increasing the length, width, and height of ...the smaller box by the same length so that the...

Cookies are packaged in boxes that measure 18cm by 20cm by 6cm. A larger box is being designed by increasing the length, width, and height of ...

the smaller box by the same length so that the volume is at least 5280 cm^3. What are the minimum dimensions of the larger box?

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The volume of a box is calculated by V = length times width times height.  The volume of the box is V=(18)(20)(6). The volume of the larger box is V=(18+x)(20+x)(6+x) where x represents the increase for each edge. The inequality needed to be solved to find x is:

`(x+18)(x+20)(x+6)>=5280`

`(x^2+38x+360)(x+6)>=5280`

`x^3+44x^2+588x+2160>=5280`

`x^3+44x^2+588x-3120>=0`

Graphing the polynomial, the only x-intercept is at x=4.

The dimensions of the larger box are: 18+4=22, 20+4=24, and 6+4=10.

22 cm, 24 cm, and 10 cm.

 

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