Question 1163171
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The area of the plate is  A = {{{pi*r^2}}},

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


    A(t) = {{{pi*r^2(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



<U>ANSWER</U>.  A'(t) = 2*pi*2.5*0.01 = 2*3.14159*2.5*0.01 = 0.157 cm^2/s.
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Solved, answered, explained.