Question

PLEASE HELP!

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) (x−7)(x−11)x
B) (7−2x)(11−2x)x
C) (11−7x)(11x−7)
D) (7x−11)(7−11x)

Answer 1

Answer: B)
`(7-2x)(11-2x)x`

Explanation:

Given: The length of the cardboard = 11 in.

The width of the cardboard =7 in.

If a box is created without a top from a piece of cardboard, but cutting out square corners with side length x, then the dimensions of box will be:-

Width (w)=
`7-2x`

length (l)=
`11-2x`

Height (h)=
`x`

Now, volume of rectangular box is given by :-

`V=lwh\\\\\Rightarrow\ V=x(7-2x)(11-2x)`

Hence, the expression can be used to determine the greatest possible volume of the cardboard box is given by :-

`(7-2x)(11-2x)x`

Answer 2

Option B

Explanation:

Given is a rectangle with width 7 and length 11.

From each corner of the rectangle a square of length x is cut and foled to make a box

Now for the open box we made, height = x

width = rectangle width - 2 times d

= 11-2x

Length = rectangle length-2x

Hence volume of box

=lwh

= (7-2x)(11-2x)x