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.? _________
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
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)
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.