SOLUTION: please help A circular plate is cooled and contracts so its radius is shrinking by 0.01cm/s. How fast is the area of one face changing when the radius is 2.5cm? Round to 3 si

The area of the plate is  A = ,

or, since the radius depends on time  r = r(t),  the area is


    A(t) = .      (1)


The derivative A'(t) is


    A'(t) = 2*pi*r(t)*r'(t).     (2)


We are given  r'(t) = 0.01 sm/s  and  r(t) = 2.5 cm.  Substitute these values into the formula (2) and get the



ANSWER.  A'(t) = 2*pi*2.5*0.01 = 2*3.14159*2.5*0.01 = 0.157 cm^2/s.