The radius r and height h of a cylinder are changing with time. At the instant in question, r = 3 cm, h = 4 cm, dr/dt = 0.02 cm/sec an dh/dt = -0.03 cm/sec. At what rate is the cylinder's volume changing at that instant?

The area of a circle increases at a rate of 2 cm² /s. How fast is the radius changing when the radius is 5cm? a) Draw the picture. b) Write the given and unknown derivatives in d/dt notation. c) Label the variables. d) Proceed to solve and finish the problem. Reminder, keep solutions and answer in exact form and don't forget the units on the final answer.