5. Oil is leaking from a pipeline on the surface of Laguna Lake and forms an...

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5. Oil is leaking from a pipeline on the surface of Laguna Lake and forms an oil slick whose volume increases at a constant rate of 2000 cm/min. The oil slick takes the form of a right circular cylinder with both its radius and height changing with time. a.) At the instant when the radius of the oil slick is 100 centimeters and the height is 0.6 cm, the radius is increasing at the rate of 2.5 cm/min. At this instant, what is the rate of change of the height of the oil slick with respect to time, in cm/min? b.) A recovery device arrives on the scene and begins removing oil. The rate at which oil is removed R(t) = 400t cm/min, where t is the time in minutes since the device began working. Oil continues to leak at the rate of 2000 cm/min. Find the time t when the oil slick reaches its maximum volume. 5. Oil is leaking from a pipeline on the surface of Laguna Lake and forms an oil slick whose volume increases at a constant rate of 2000 cm/min. The oil slick takes the form of a right circular cylinder with both its radius and height changing with time. a.) At the instant when the radius of the oil slick is 100 centimeters and the height is 0.6 cm, the radius is increasing at the rate of 2.5 cm/min. At this instant, what is the rate of change of the height of the oil slick with respect to time, in cm/min? b.) A recovery device arrives on the scene and begins removing oil. The rate at which oil is removed R(t) = 400t cm/min, where t is the time in minutes since the device began working. Oil continues to leak at the rate of 2000 cm/min. Find the time t when the oil slick reaches its maximum volume.