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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)

Guest Apr 11, 2018

Best Answer 

 #1
avatar+7164 
+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
 #1
avatar+7164 
+1
Best Answer

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

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