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# Need Some help

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A company is creating a box without a top from a piece of cardboard, but cutting out square corners with side length x.

Which expression can be used to determine the greatest possible volume of the cardboard box?

A.) (15−x)(22−x)x

B.) (x−15)(x−22)x

C.) (15−2x)(22−2x)x

D.) (22x−15)(15x−22)

Apr 11, 2018

#1
+7616
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volume of box   =   (width)(length)(height)

width   =   15 - x - x

width   =   15 - 2x

length   =   22 - x - x

length   =   22 - 2x

height   =   x

volume of box   =   (width)(length)(height)

volume of box   =   (15 - 2x)(22 - 2x)x

The expression  (15 - 2x)(22 - 2x)x  can be used to determine the volume of the box.

(  And by looking at a graph we can see that the greatest possible volume is about  432 in3 .

Here's a graph:   https://www.desmos.com/calculator/h7gylso5p9

And note that the length of  x  can't actually be greater than  15/2 in.  )

Apr 11, 2018
edited by hectictar  Apr 11, 2018
edited by hectictar  Apr 11, 2018

#1
+7616
+1

volume of box   =   (width)(length)(height)

width   =   15 - x - x

width   =   15 - 2x

length   =   22 - x - x

length   =   22 - 2x

height   =   x

volume of box   =   (width)(length)(height)

volume of box   =   (15 - 2x)(22 - 2x)x

The expression  (15 - 2x)(22 - 2x)x  can be used to determine the volume of the box.

(  And by looking at a graph we can see that the greatest possible volume is about  432 in3 .

Here's a graph:   https://www.desmos.com/calculator/h7gylso5p9

And note that the length of  x  can't actually be greater than  15/2 in.  )

hectictar Apr 11, 2018
edited by hectictar  Apr 11, 2018
edited by hectictar  Apr 11, 2018