Question

PLEASE HELP ASAP!!!! I'm stuck and any help is appreciated

A box without a top is made from a rectangular piece of cardboard, with dimensions 40 inches by 32 inches, by cutting out square corners with side length x inches.


Which expression represents the volume of the box in terms of x?


A.) (40−2x)(32−2x)x


B.) (40−2x)(32−2x)4x


C.) (40−x)(32−x)x


D.) (2x−40)(2x−32)x

Answer 1

The expression is (40 − 2x)(32 − 2x)x ⇒ answe A

Explanation:

* Lets study the information of the problem

- The rectangular piece of cardboard has dimensions 40 inches

and 32 inches

- A square of side length x is cutting from each corner

- That means we cut x from each sides of length and width,

x from left corner and x from right corner

∴ The new length = 40 - x - x = 40 -2x

∴ The new width = 32 - x - x = 32 - 2x

* Now when we fold the cardboard to make the box we will stick

the sides of length x together to make the heights of the box

∴ The height of the box = x

- The volume of the box = area of its base × its height

∵ The length of the base is (40 - 2x)

∵ The width of the base is (32 - 2x)

∴ The area of the base = (40 - 2x)(32 - 2x)

∵ The height of the box is x

∴ The volume of the box = (40 - 2x)(32 - 2x)x

* The expression which represent the volume is (40 − 2x)(32 − 2x)x

- The attached picture will help you to understand