Related Rate (Cal)
2008-11-20 10:57 pm
Water, at the rate 10 ft^3/min, is pouring into a leaking cistern whose shape is a cone 16 ft deep and 8 ft in diameter at the top. At the time the water is 12 ft deep, the water level is observed to be rising 4 in/min. How fast is the water leaking away? (in terms of pi)
回答 (2)
2008-11-21 12:33 am
✔ 最佳答案
Let volume running in = Vwater leaking out = U
so V - U = (1/3)pr^2h where p = pi............(1)
By similar triangle, r/h = 4/16, therefore, r = h/4, sub. into (1), we get
V - U = (1/3)p(h/4)^2h = (1/48)ph^3
dV/dt - dU/dt = (1/48)p(3h^2)dh/dt.
Now dV/dt = 10, h = 12, dh/dt = (1/3), therefore,
10 - dU/dt = (1/48)p(3)(144)(1/3) = 3p
dU/dt = (10 - 3p ) ft^3/min.
2008-11-21 12:26 am
The answer is as follows:
圖片參考：http://i277.photobucket.com/albums/kk75/uncle_michael/20081120_mat_1.jpg?t=1227169536
圖片參考：http://i277.photobucket.com/albums/kk75/uncle_michael/20081120_mat_1.jpg?t=1227169536
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