A circle has an initial radius of 50 ft when the radius begins decreasing at the rate of 5 5 ft/min. What is the rate in the ch ange of area at the instant that the radius is 26 26 ft?
1 answer:
Answer:
-816.8 ft²/min
Step-by-step explanation:
The rate of change of area is the product of the rate of change of radius and the circumference of the circle. At the time of interest, ...
dA/dt = C·dr/dt = 2πr·dr/dt
dA/dt = 2π·(26 ft)(-5 ft/min)
dA/dt = -260π ft²/min ≈ -816.8 ft²/min
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