Question

A spherical balloon , initially inflated to a volume of over 30000 cubic meters, springs a leak which causes the radius to decrease at a rate of 2 meters per minute. At the instant when the radius is 3 meters , how fast ( in cubic meters per minute ) is the hor air escaping from the balloon?

Answer 1

VOLUME=4/3 pi R^3
dV/dt=4/3 pi 3r^2 dr/dt=4PIr^2 dr/dt

Put in dr/dt, r, and calculate dv/dt