Hello, Tubaman!
The volume of a cone is: .
Since , we have: .
Differentiate with respect to time: .
We are told that:
Hence: .
Integrate: .
When
So we have: .
Therefore: .
Here is the problem I'm trying to solve:
The volume of a conical pile of sand is increasing at a rate of 243(pi)ft^3/min, and the height of the pile always equals the radius r of the base. Express r as a function of time t (in minutes), assuming that r = 0 when t = 0.
I'm not even sure how to set this one up! Please help!
Soroban,
Thanks much for your response. However, this problem was presented within a chapter regarding composite functions; that is, to solve the problem using "nested" functions. Is it possible to present a solution that utilizes this method, and that also employs no calculus?
Thanks!
Tubaman