(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

2. Coffee is draining from a conical filter into a cylindrical coffee pot at the rate of 10 in3/min.

a) How fast is the level in the pot rising? ____________

b) How fast is the level in the cone falling when the level in the cone is 5 in.? _________

2. Relevant equations

i know i need to use the volume formulas for a cylinder and a cone, but i dont know how to differentiate them. heres the wrong answers i got:

V= pi(r^2)h --> d/dt[V]= pi(2r)(dh/dt)--> dV/dt= 2(pi)(r)*dh/dt

dh/dt= (1/(2(pi)(r)))*dV/dt

dV/dt= 2/3(pi)(r)(dh/dt)

3/(2(pi)(r))*(dV/dt)

3. The attempt at a solution

when i differentiate both sides with respect to time i get:

d/dt[V]= 2/3(Pi)(r)*(dh/dt) ---> dV/dt= 2/3(pi)(r)(dh/dt)

dh/dt= 3/(2(pi)(r))*(dV/dt)

dh/dt= 3/(2(pi)(r))*(10in^3/min)

30/2(pi)r = 15/(pi)(r) in^3/min

p.s. this is really getting frustrating. if calc 1 is throwing me curveballs like this that i cant solve, my quest to be a mechanical engineer seams very bleak.

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