AMATHS一條f.4(application of differentiation)

👨🏻‍🏫 學術台 數學
2008-06-18 5:39 am
consider a trough 2m long and with ends that are equilateral triangles, if water is flowing in at the rate of" 開方3"m^3/min,how fast is the water level rising
when the depth of the water is 0.5m?
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回答 (1)

2008-06-18 6:42 am
✔ 最佳答案
Let side of equilateral triangle = a, and height of equilateral triangle = h.
Therefore, (a/2)/h = tan30. a = 2htan30. Therefore, area of triangle = ah/2 = h^2tan30.
Therefore, volume of trough = (2)h^2tan30 = V.
Therefore, dV/dt = 4tan30(h)(dh/dt).
Now dV/dt = sqrt3, h = 0.5, tan30 = 1/sqrt3. Therefore, dh/dt = (sqrt3)(sqrt3)/(4 x 0.5) = 3/2 m/min.
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