1.a right circular conical vessel with the semi-vertical angle of 45度 is placed on a horizontal table with its apex upwards. water is poured into the vessel through a small hole in the apex, at a uniform rate of 12cm3/s.
a)find the rate at which the level of the water is rising when the surface of the water is 6cm below the apex. Ans=1/3派cm3/s
b)find the rate at which the area of the surface of the water is decreasing at that moment. Ans=4cm2/s
amaths
2007-11-09 2:50 am
回答 (1)
2007-11-09 4:40 am
✔ 最佳答案
a)h / r = tan 45*So h = r
V = πr2h / 3
= πh3 / 3
dV / dt = (π/ 3 )( 3h2 )( dh / dt )
= πh2 ( dh / dt )
12 = π( 6 )2 ( dh / dt )
dh / dt = 12 / 36π
= 1/3π
So the level of the water is rising at 1/3πcm/s.
b)A=πr2
=πh2
dA / dt = 2πh ( dh / dt )
dA / dt = 2π( 6 )( 1 / 3π)
= 4
So the area of the surface of the water is decreasing at 4cm2/s.
參考: My Maths Knowledge
收錄日期: 2021-04-13 14:22:59
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