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Oil is leaking from a pipeline on the surface of a lake and forms an oil slick whose volume
increases at a constant rate of 1500 cubic centimeters per minute. The oil slick takes the
form of a right circular cylinder with both its radius and height changing with time. At the
instant when the radius of the oil slick is 200 centimeters and the height is 2 centimeters,
the radius is increasing at the rate of 4 centimeters per minute. At this instant, what is the
rate of change of the height of the oil slick with respect to time, in centimeters per minute?
(The volume of a right circular cylinder with radius r and height h is given by V = πr²h.)
Sagot :
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