An Open Box Is to Be Made from a Square $x ^ { 2 }$

question 31

Multiple Choice

An open box is to be made from a square piece of cardboard having dimensions 32 inches by 32 inches by cutting out squares of area $x ^ { 2 }$ from each corner as shown in the figure below. Express the volume V of the box as a function of x. $$32 - 2 x$$ $$32 - 2 x$$

• A) \(V ( x ) = 32 x ^ { 2 } - 2 x ^ { 3 }\)
• B) \(V ( x ) = 32 x - 64 x ^ { 2 } + 4 x ^ { 3 }\)
• C) \(V ( x ) = 1024 - 128 x + 4 x ^ { 2 }\)
• D) \(V ( x ) = 1024 x - 128 x ^ { 2 } + 4 x ^ { 3 }\)
• E) \(V ( x ) = 1024 x - 64 x ^ { 2 } + 4 x ^ { 3 }\)

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Definitions:

Substitute

In a legal or contractual context, to replace one obligation, duty, or individual with another.

Cash

represents money in the physical form of currency, such as coins and banknotes, used to purchase goods, services, or settle debts.

Certify

To officially recognize, verify, or declare something as true, accurate, or in compliance with certain standards.

Sufficient Funds

Availability of enough money or resources to meet financial obligations or complete transactions.