If the radius of the circle changes at the rate of m/sec, at what rate does the circle's area change when the radius is 10 m?

-40 m²/sec Explanation: Concept: - The area of a circle with r units, is: sq. units. - The rate of change of the value of a function f(x) with respect to a variable t, is given by: . - Chain Rule of Derivatives: . - . Calculation: Let's say that the radius of the circle is r meters and let t be the time in seconds. It is given that m/sec. Now, Area of the circle: m². Using the chain rule of derivatives: When the radius is , the rate of change of area will be: ** **. NOTE: A negative value of the rate of change indicates a decrease.

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