a. maths Rate of Change 急..!!
2009-05-15 2:49 am
Water is pumped out at a rate of 3 m^3min^-1 from a hemispherical water tank with r=13 m. 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 8 m?
回答 (1)
2009-05-15 3:23 am
✔ 最佳答案
Let the volume of the hemispherical water tank be V m^3when the depth of the water is x m ,
V=( π/3 )x^2(39-x) ...(*)
differentiate (*) w.r.t. time
dV/dt=( π/3 )[x^2(-1)+(39-x)(2x)](dx/dt)
put dV/dt=-3 , x=8
dx/dt=-6.63*10^(-3)
That is , the water level drops at a rate of 6.63*10^(-3) m/min
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