Question

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?

Answer 1

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