+0  
 
0
64
1
avatar

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+6943 
+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
Sort: 

1+0 Answers

 #1
avatar+6943 
+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

10 Online Users

We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details