��Example: 1�Gas is escaping from a spherical balloon at the rate of 2 ft3 / min .How fast is the surface area shrinking when the radius is 12 ft ? ��

Answer 1

given that V'=2ft^3/min;r=12ft,V=(4pi r^3)/3,S=4pi r^2.
dV/dr=4pir^2; dS/dr=8pi r
dS/dt=dS/dr x V'/(dV/dr)
dS/dt=(8pi r x 2)/4pi r^2=1/3
dS/dt=1/3 ft^2/min