Question

Helium is pumped into a spherical balloon at a rate of 3 cubic feet per second. How fast is the radius increasing after 2 minutes?
Note: The volume of a sphere is given by V=(4/3)πr^3

Answer 1

differentiate volume equation wrt "t"

\[\frac{dV}{dt} = 4 \pi r^2 \frac{dr}{dt}\]
dV/dt = 3
if initial volume is 0 then after 2 min (120 sec) the new volume is 360
solve for radius , plug into derivative equation to find dr/dt