Assignment:
Sand falls from an overhead hopper to form a right circular cone. If the cone formed has an angle α find the rate of change of volume with respect to height? If the height is changing at 2cms per minute, what volume of sand is falling from the hopper when the height of the cone is 3 meters? (The volume of a cone is (1/3)πr2h where h is the height and r is the radius.)
Provide complete and step by step solution for the question and show calculations and use formulas.