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 change of area at the instant that the radius is 26 26 ft?

-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