calculus
posted by james on .
a spherical balloon filled with gas has a leak that permits the gas to escape at a rate of 1.5 cubic meters per minute. how fast is the surface area of the balloon shrinking when the radius is 4 meters?

v = 4/3 pi r^3
dv/dt = 4pi r^2 dr/dt
1.5 = 4pi (16) dr/dt
dr/dt = 1.5/64pi
a = 4pi r^2
da/dt = 8pi r dr/dt
= 8pi (4) (1.5/64pi)
= 3/4 m^2/min