Precalculus
posted by Jim on .
From a rectangular piece of cardboard having dimensions a × b, where a = 40 inches and b = 70 inches, an open box is to be made by cutting out an identical square of area x2 from each corner and turning up the sides (see the figure). Express the volume V of the box in terms of x. (Factor your answer completely.)

after turning up the corners, the bottom now measures
(a2x)(b2x)
The depth of the box is the size of the tabs folded up, or x
V = (a2x)(b2x)(x)
= x(402x)(702x)
= 4x(20x)(35x)