An Open Box Is to Be Made from a Square $V ( x ) = - 2 x ^ { 3 } + 28 x ^ { 2 }$

question 337

Multiple Choice

An open box is to be made from a square piece of cardboard, 28 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) \(V ( x ) = - 2 x ^ { 3 } + 28 x ^ { 2 }\)
• B) \(V ( x ) = - 4 x ^ { 3 } + 56 x ^ { 2 }\)
• C) \(V ( x ) = 4 x ^ { 3 } - 56 x ^ { 2 } + 28 x\)
• D) \(V ( x ) = - 4 x ^ { 3 } + 56 x ^ { 2 } - 28 x\)
• E) \(V ( x ) = 4 x ^ { 3 } - 112 x ^ { 2 } + 784 x\)

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Definitions:

Seed

A plant's unit of reproduction, capable of developing into another such plant, containing an embryo along with a food supply encased in a protective outer covering.

Compound Fruits

Fruits that develop from multiple flowers (inflorescence) or from a single flower with multiple ovaries, forming a single mass.

Carpels

The female reproductive organs of a flower, comprising the stigma, style, and ovary.

Legumes

A group of plants, including beans, peas, and lentils, that have the ability to fix nitrogen from the air into the soil, improving soil fertility.