Solve the following using related rates and show all steps of working

1. A cylindrical tank with radius5m is being filled with water at a rate of 2m³/min. How fast is the height of the water increasing? Answer: m/min

2. The radius of a sphere is increasing at a rate of3mm/s. How fast is the volume increasing when the diameter is60mm? Answer: mm³/s

3. A plane flying horizontally at an altitude of 2 mi and a speed of 540 mi/h passes directly over a radar station. Find the rate at which the distance from the plane to the station is increasing when it has a total distance of 5 mi away from the station. (Round your answer to the nearest whole number.) Answer: mi/h

4. Two cars start moving from the same point. One travels south at 24 mi/h and the other travels west at 18 mi/h. At what rate is the distance between the cars increasing three hours later? Answer: mi/h

5. Gravel is being dumped from a conveyor belt at a rate of30ft³/min, and its coarseness is such that it forms a pile in the shape of a cone whose base diameter and height are always equal. How fast is the height of the pile increasing when the pile is9ft high? (Round your answer to two decimal places.) Answer: ft/min

6. This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to come back to the skipped part.