Question

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?



(15−x)(22−x)x


(x−15)(x−22)x


(15−2x)(22−2x)x


(22x−15)(15x−22)

Answer 1

(15−2x)(22−2x)x

Answer 2

Volume of box = (15−2x)(22−2x)x

C is correct.

Explanation:

A company is creating a box without a top from a piece of cardboard, but cutting out square corners with side length x.

The dimension of the cardboard must be 15 x 22 because all options has same value.

We have rectangle cardboard with 15 x 22. We cut square from each corner of the board with dimension x.

New length of box = 22 - 2x

New Width of box = 15 - 2x

Height of the box = x

Volume of box is equal to volume of cuboid.

Volume of box = LBH

= (15-2x)(22-2x)(x)

Hence, The correct volume of the box is (15-2x)(22-2x)(x)