An Open Box Is to Be Made from a Square $V ( x ) = - 4 x ^ { 3 } + 66 x ^ { 2 } - 33 x$

Multiple Choice

An open box is to be made from a square piece of cardboard, 33 inches on a side, by cutting equal squares with sides of length x from the corners and turning up the sides (see figure below) .Determine the function, V, in terms of x, that represents the volume of the box.

A) $V ( x ) = - 4 x ^ { 3 } + 66 x ^ { 2 } - 33 x$
B) $V ( x ) = - 2 x ^ { 3 } + 33 x ^ { 2 }$
C) $V ( x ) = 4 x ^ { 3 } - 132 x ^ { 2 } + 1089 x$
D) $V ( x ) = - 4 x ^ { 3 } + 66 x ^ { 2 }$
E) $V ( x ) = 4 x ^ { 3 } - 66 x ^ { 2 } + 33 x$