- #1
billmccai
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Homework Statement
A water tank is in the shape of an inverted conical cone with top radius of 20m and
depth of 15m. Water is flowing into the tank at a rate of 0.1m^3/min.
(a) How fast is the depth of water in the tank increasing when the depth is 5m?
Water is now leaking from the tank at a rate that depends on the depth h, (h= height of
water in the tank) this rate is 0.1h^3/min.
(b) How fast is the depth of water in the tank changing when the depth is 5m?
(c) How full can the tank get?
Homework Equations
The Attempt at a Solution
Ok for part A:
Tan(angle) = 20/15 = 3/4
So i got a formula for r... r = 4/3 h
Which i put into the formula for the volume of a cone and got:
V = 16pi/27 * h^3
and then differentiated V with respect to time.
dV/dt = 16pi/27 * (3h^2)dh/dt
and i know h and dV/dt so i subbed those in and got
dh/dt = 7.1697 * 10^(-4) m/min
which I'm pretty sure is right.
Now I'm not sure how to do part b.
Do I set dV/dt as 0.1 - 0.1h^3
and then just do the same thing? Or is this wrong. Also, what about part c?
I tend to get a bit lost with these sorts of wordy questions. Please help.