Question

RATES OF CHANGE QUESTION

A spherical balloon is being blown up so that its volume is increasing by 0.6 m^3 s^-1. Find the rate at which the radius is increasing when the radius is 0.1 m.

So what I did was that I determined dV/dt =0.6
and dV/dr = 4/3 r^3 phi (which is the volume of a sphere), and I should calculate dr/dt.

The answer should be 15 / phi but I figured I'll have to inverse the dV/dr part in order to get dr/dt.
But how do I do this???

Answer 1

Hmmm you just have to invert the answer that all

Answer 2

sure I did but I do not get 15/phi.

Answer 3

We know
V = (4/3)πr^3

Just differentiate with respect to t

dV/dt = 4πr^2 dr/dt

now sub in our values

.6 = 4π(.1)^2 dr/dt
.6/(.04π = dr/dt
dr/dt = 15/π