Water Is Pouring Into A Cone At 3 Ft3/minute. The

Anonymous

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Water is pouring into a cone at 3 ft3/minute. The cone has a radius of 5 feet and a height of 12 feet. Find how fast the water is rising when a) the water level is 1ft high and b) the water level is 11ft high. Explain why these two rates the differ the way that they do. (Vcone= (1/3)Pir2h)

 

Answer No.1

EliteDan77

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V = pr^2h/3 => dV/dt = p/3 [ h.2r.dr/dt + r^2.dh/dt ]............(1) we know, dr/dt = 0, because it is a fixed cone generally. hence, only variable is dh/dt. from (1), 3 = p/3 [ 2.5.12(0) + (5)^2.dh/dt ] 3 = p/3 [ 25.dh/dt ] => dh/dt = 9/(25p)

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