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Sand is poured into a right conical pile with the height of the pile equaling the diameter of the pile, which stands upright vertically and
Sand is poured into a right conical pile with the height of the pile equaling the diameter of the pile, which stands upright vertically and the circular base opens upward. If the sand is poured at a constant rate of 5 cubic meters per second (m3 /s), at what rate is the height of the pile increasing when the height is 2 meters (m.)? (Answer in terms of it ). [ Hint: Let V (m.3) be the volume of the sand in the conical pile, r (m.) be the radius of the circular base of the sand, and h (m.) be the height of the sand in the pile. Then, V = $111"sz and h = 2r . ]
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