Solve the Problem $3 \mathrm {~cm}$ Squares from Each Corner and Folding Up the Sides

question 431

Multiple Choice

Solve the problem.
-A piece of cardboard is twice as long as it is wide. It is to be made into a box with an open top by cutting $3 \mathrm {~cm}$ squares from each corner and folding up the sides. Let $x$ represent the width of the original piece of cardboard. Determine a function $\mathrm { V }$ that represents the volume of the box in terms of $x$ .

• A) \(V ( x ) = 6 x ^ { 2 }\)
• B) \(V ( x ) = 3 x ^ { 2 } - 36 x + 108\)
• C) \(V ( x ) = 6 x ^ { 2 } - 27 x + 27\)
• D) \(V ( x ) = 6 x ^ { 2 } - 54 x + 108\)

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Definitions:

Net Operating Income

The earnings a business retains after subtracting operational costs, prior to the deduction of interest and taxes.

Total Contribution Margin

The difference between a company's sales revenue and variable costs, representing the amount available to cover fixed costs and contribute to profit.

Net Operating Income

A measure of a company's profitability excluding interest and tax expenses.

Operating Income

This is the profit realized from a business's operations, calculated by subtracting operating expenses from gross profit.