Question

thank you very much

Water is leaking out of an inverted conical tank at a rate of 11,000 cm3/min
at the same time that water is being pumped into the tank at a constant
rate. The tank has height 6 m and the diameter at the top is 4 m. If
the water level is rising at a rate of 20 cm/min when the height of the
water is 2 m, find the rate at which water is being pumped into the
tank. (Round your answer to the nearest integer.)

Answer 1

水从一个倒圆锥状的箱里以11000 cm3/分钟的速度流出来。同一时间，水以一个不变的速度被泵入箱里。这个箱子高6m,顶部的直径长4m。如果水位上升的速度为20cm/分钟时水深2m。求水被泵入箱子的速度。（把答案约到最近的整数）

追问

我能看懂 就是不会算!

追答

半径：高度 = 2m:6m
r(2m高的半径)：2m →r = (2/3)m

2m时面积 = πr^2 = π(2/3m)^2 = (4/9)πm^2 = (40000/9)πcm^2
速度：20cm/min*(40000/9)πcm^2 = (800000/9)πcm^3/min = 279252.68cm^3/min

279252.68cm^3/min = v - 11000cm^3/min
v = 290252cm^3/min

答案正确不，好久没做这些题了。。。

追问

不对啊 我还有两次机会

追答

v = 290253cm^3/min

对不起，忘记小数点往上约了。这个应该是答案了。
顺便一提，如果π是按3.14算，那么答案是290111cm^3/min。

Answer 2

V=H*A=20cm*pi*(4/2)^2= 2513274cm3
so the water increasing at the rate of 2513274cm3/min,
the water is being pumped in = water increase + water leaking = 2513274cm3/min +11000cm3/min= 3613274cm3/min

追问

答案不对啊