Answer:
The rate of change of radius is 0.0530 ft/sec.
Step-by-step explanation:
Given : Helium is pumped into a spherical balloon at a rate of 3 cubic feet per second.
To find : How fast is the radius increasing after 2 minutes?
Solution :
The volume of the sphere is
Differentiating w.r.t. r,
We have given, Helium is pumped into a spherical balloon at a rate of 3 cubic feet per second.
i.e.
Integrate w.r.t. t,
Assuming V=0 when t=0 then C=0
So,
Now, we apply chain rule
i.e.
The radius increasing after 2 minutes i.e. at
Therefore, the rate of change of radius is 0.0530 ft/sec.