An Open Box Is to Be Made from a Square $12 ^ {||}$

question 50

Multiple Choice

An open box is to be made from a square piece of cardboard, 36 inches on a side, by cutting equal squares with sides of length x from the corners and turning up the sides (see figure below) . After determining the function V, in terms of x, that represents the volume of the box, use a graphing utility to estimate the dimensions that will maximize its volume.

• A) \(12 ^ {||}\) × \(12 ^ { ||}\) × \(6^{||}\)
• B) \(24^{||}\) × \(24^{||}\) × \(6^{||}\)
• C) \(24^{||}\) × \(24^{||}\) × \(12 ^ { || }\)
• D) \(18^ { ||}\) × \(18^ { ||}\) × \(12^ { ||}\)
• E) \(6^ { ||}\) × \(6^ { ||}\) × \(3^ { ||}\)

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Definitions:

Sample Size

The number of subjects or units chosen from a population to participate in a study.

Accurate

A term describing the closeness of a measurement to the true value or the degree of accuracy of a measurement or process.

Sample Estimates

Statistical values calculated from a sample that estimate corresponding parameters in the population from which the sample is drawn.

Observational Study

A study where the researcher observes and records behavior or outcomes without actively manipulating variables or conditions.