Water is pumped out at a rate if 3 m^2/min from a hemisphere water tank with radius 13m. When the depth of water is x m, the volume of water inside the tank is (π/3)x^2(39-x) m^3. At what rate is the water level dropping when the depth of water is 8m?
Ans: 1/48π m/min
Rate of change
2011-01-19 9:12 pm
回答 (1)
2011-01-19 9:25 pm
✔ 最佳答案
V=(π/3)x^2(39-x)V=(π/3)(39x^2-x^3)
Differentiate both sides w.r.t. t
dV/dt=(π/3)(39*2x*(dx/dt)-3x^2*(dx/dt))
dV/dt=(π/3)(78x-3x^2)(dx/dt)
-3=(π/3)*432*(dx/dt)
dx/dt=-1/48π m/min
2011-01-19 16:08:38 補充：
For step3, just sub. x=8 and dV/dt=-3
2011-01-19 20:10:10 補充：
Yes........................
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