Question

A square has sides of 16 units. Squares x + 1 by x + 1 units are cut out of each corner, and then the sides are folded up to create an open box. Express the volume V of the box as a function in terms of x.

V(x)=

Answer 1

A distance of (x+1) is cut in from both sides, so the base dimensions are

... 16 -2(x+1) = 14-2x

The depth of the fold is (x+1), so that is the depth of the box.

The volume is ...

... V(x) = (x+1)(14 -2x)²