how fast if the radius increasing

Question

Helium is pumped into a spherical balloon at a rate of 5 cubic feet per second. How fast is the radius increasing after 2 minutes? 


Rate of change of radius (in feet per second) = 

Answer 1

I agree with dV/dt, to finish the question you just need to plug in 5ft³/s into the equation, as well as r.  At 2 seconds the volume of the balloon is 10ft³.  If you assume the balloon is a sphere then;

 

V=4/3πr³

10=4/3πr³

(30/4π)^1/3=r 

 

 

5=4π(30/4π)^2/3dr/dt

 

just solve for dr/dt

Answer 2

This is a related rates problem. It asks us to find dr/dt when t = 2.

 

We are given that dV/dt = 5 ft³

 

We can use the volume of a sphere formula: V = 4/3πr³. If we differentiate both sides with respect to t, we get:

 

dV/dt = 4πr² dr/dt

 

Is there any mention about the length of the radius (or diameter), Hussein?