SOLUTION: Hi, Please can somebody help with this, The base radius r cm of a right-circular cone increases at 2 cm s^-1 and its height h cm at 3 cm s^-1. Show that the rate of increase in

Question 383221: Hi, Please can somebody help with this,
The base radius r cm of a right-circular cone increases at 2 cm s^-1 and its height h cm at 3 cm s^-1. Show that the rate of increase in its volume V = 1/3 pi r^2h when r = 5 and h = 15 is 125 pi cm^3 s^-1.
Thank You
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
We have
(separating all the constants)
h and r are both functions in terms of time, t. We can take dV/dt by the product rule:

At this instant, we have , , , and . Substituting all of the known variables in, we obtain

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