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

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> 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       Log On


   

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) About Me  (Show Source):
You can put this solution on YOUR website!
We have
V+=+%28pi%2F3%29%28hr%5E2%29 (separating all the constants)
h and r are both functions in terms of time, t. We can take dV/dt by the product rule:
dV%2Fdt+=+%28pi%2F3%29%28%28dh%2Fdt%29r%5E2+%2B+h%2A%282r%29%2A%28dr%2Fdt%29%29
At this instant, we have dh%2Fdt+=+3+cm%2Fs, h+=+15+cm, dr%2Fdt+=+2+cm%2Fs, and r+=+5+cm. Substituting all of the known variables in, we obtain