Expert: Paul Klarreich - 10/28/2008

Question
A can in the shape of a right circular cylinder with radius 8 in. is being filled at a constant rate. If the fluid is rising at a rate of 0.1 in/sec, what is the rate at which the fluid is flowing into the can? I'm confused at how to set up the problem and what equations to use.

Answer
Questioner:   Bethany
Category:  Calculus
Private:  No
 
Subject:  Calculus and Related Rates
Question:  A can in the shape of a right circular cylinder with radius 8 in. is being filled at a constant rate. If the fluid is rising at a rate of 0.1 in/sec, what is the rate at which the fluid is flowing into the can? I'm confused at how to set up the problem and what equations to use.
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Hi, Bethany,

Is this your first attempt at R-R problems?  If so, the scheme is something like this:

1. Identify the variables in the problem -- the things that change.  Give them names.

2. Write their rates of change as derivatives WITH RESPECT TO time.  Note which are known and which is to be found.

3. Determine a relationship (yes, it is called 'related rates' for a reason) between the variables.  Use a diagram, use your life experience, use your general knowledge and brilliance, do whatever you have to.  This is the key step.

4. Now differentiate implicitly, then substitute the known quantities and rates, and solve for the unknown rate.

AND, Please check the archives for other Related Rates examples.  There are a TON of them.  Click BROWSE PAST ANSWERS and look for the subject line Related Rates.



Variables :

h = height of water in the can.
V = volume ....................

Rates:

dh/dt, given as 0.1 in/sec
dV/dt, TO BE FOUND.

Relation:

V = pi r^2 h, but  r = 8, so:

V = 64 pi h.

Differentiate:

dV/dt = 64 pi dh/dt

Substitute, compute, done.