Raymond B. answered • 02/18/20
Math, microeconomics or criminal justice
468 pi cm^2/min
Area of a circle = A = (pi)r^2 = pi times radius squared
The rate of change of area is A'=dA/dt = 2(pi)rr' the first derivative of A with respect to time
A'=2(pi)rr'=2(pi)(39)(6)=468 pi square centimeters per minute
A'=468 cm^2/min
Just to check the answer, calculate the Area when r=39, A=pir^2=pi(39)^2=1521pi
In one minute r increases from 39 to 45, then A=pir^2=pi(45)^2 = 2025pi an increase of 504 pi cm^2/min
That's close to 468 pi. It shouldn't be the same as the 468 pi is the rate of change at one instant in time, while the 504 pi is for an interval of time of one minute. But it's in the right range for a correct answer.
