A spherical balloon is filled with cubic meters of helium gas. If a leak in the balloon causes the gas to escape at the rate of cubic meters per minute, then the rate (in meters per minute) at which the radius of the balloon decreases minutes after the leakage began is:
- A
- B
- C
- D
Solution & Step-by-step Explanation
Let be the volume and be the radius. .Initial volume .Rate of leakage .Volume after minutes:
Find at this volume:
Now, differentiate with respect to :
Substituting the known values:
The rate of decrease is .
Find at this volume:
Now, differentiate with respect to :
Substituting the known values:
The rate of decrease is .