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

question 242

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) \(V ( x ) = 4 x ^ { 3 } - 66 x ^ { 2 } + 33 x\)

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