A Mold Culture in a Dorm Refrigerator Is Circular and Growing

question 20

Multiple Choice

A mold culture in a dorm refrigerator is circular and growing. The radius is increasing at a rate of 0.1 cm/day. How fast is the area growing when the culture is 6 centimeters in radius (The area of a disc of radius r is $A = \pi r ^ { 2 }$ .)

• A) \(\frac { \mathrm { d } A } { \mathrm {~d} t } = 18 \pi \frac { \mathrm { cm } } { \mathrm { day } }\)
• B) \(\frac { \mathrm { d } A } { \mathrm {~d} t } = 0.6 \pi \frac { \mathrm { cm } } { \mathrm { day } }\)
• C) \(\frac { \mathrm { d } A } { \mathrm {~d} t } = 2.4 \pi \frac { \mathrm { cm } } { \mathrm { day } }\)
• D) \(\frac { \mathrm { d } A } { \mathrm {~d} t } = 1.2 \pi \frac { \mathrm { cm } } { \mathrm { day } }\)
• E) \(\frac { \mathrm { d } A } { \mathrm {~d} t } = 0.2 \pi \frac { \mathrm { cm } } { \mathrm { day } }\)

Solve problems involving the relationship between variables in various formulas, including those of geometric figures like cylinders.

Apply the understanding of variation (both direct and inverse) to solve problems related to physical laws such as Hooke's Law.

Understand and apply formulas for calculating stopping distances and power generated under varying conditions.

Solve problems involving the calculation of time, distance, and rates in direct and inverse proportionality contexts.

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