Helium is pumped into a spherical balloon at a rate of 5 cubic feet per second. How fast is the radius increasing after 3 minutes?
Note: The volume of a sphere is given by V=(4/3)\pi r^3.
dV/dt = 4pir^2(dr/dt)
Time = 3 minutes (180 seconds)
how to find r?

Question

Helium is pumped into a spherical balloon at a rate of 5 cubic feet per second. How fast is the radius increasing after 3 minutes? 
Note: The volume of a sphere is given by V=(4/3)\pi r^3. 
dV/dt = 4pir^2(dr/dt)
Time = 3 minutes (180 seconds)
how to find r?

phi · Answer

we have to assume the balloon starts empty.  then after 3 minutes, it will have
180 sec * 5 ft^3/sec = 540 ft^3
i.e. that is its volume, so you can solve for r