Write the polynomial function that models the given situation.

Question

A square has sides of 18 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

Make a drawing.  The side is 18 units long.  But at each end, x+1 is subtracted out for the corner, so the length of the sides when it's folded up must be 18 - 2(x+1) = 16 -2x.

 

So you have a square base, 16-2x on each of the 4 sides, and the height of the box is x+1.

 

Using Base AREA = (16-2x)² and the aforementioned height, you can write the formula for VOLUME.