A box without a top is made from a rectangular piece of cardboard, with dimensions 27 centimeters by 18 centimeters, by cutting out square corners with side length x centimeters. Which expression represents the volume of the box in terms of x?

A. (27−2x)(18−2x)4x B. (2x−27)(2x−18)x C. (27−2x)(18−2x)x D. (27−x)(18−x)x

May 24, 2018

C. (27−2x)(18−2x)x\ "cm"^3

Explanation:

The box, when folded, will have a height of $x$ cm

The two sides of its square base will be $27 - 2 x$ cm and $18 - 2 x$ cm, respectively.

Thus the volume will be

$\left(27 - 2 x\right) \left(18 - 2 x\right) x \setminus {\text{cm}}^{3}$