Solve the Problem $500 \mathrm {~cm} ^ { 3 }$ As the Area of the Base Increases at a Rate

question 536

Multiple Choice

Solve the problem. Round your answer, if appropriate.
-The volume of a rectangular box with a square base remains constant at $500 \mathrm {~cm} ^ { 3 }$ as the area of the base increases at a rate of $6 \mathrm {~cm} ^ { 2 } / \mathrm { sec }$ . Find the rate at which the height of the box is decreasing when each side of the base is $15 \mathrm {~cm}$ long. (Do not round your answer.)

• A) \(\frac { 8 } { 9 } \mathrm {~cm} / \mathrm { sec }\)
• B) \(\frac { 2 } { 75 } \mathrm {~cm} / \mathrm { sec }\)
• C) \(\frac { 20 } { 9 } \mathrm {~cm} / \mathrm { sec }\)
• D) \(\frac { 8 } { 135 } \mathrm {~cm} / \mathrm { sec }\)

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Definitions:

Marginal Cost

The additional expense incurred from the production of one more unit of a good or service.

Competitive Level

The extent to which companies or products compete within a market, affecting prices, quality, and innovation.

Superstars

Exceptionally talented individuals in a particular field or activity who are widely recognized for their skills.

Committed

Showing a strong dedication or allegiance to a cause, activity, or job.