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

#1**+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 in^{3} .

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

#1**+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 in^{3} .

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