Question

a spherical ballon is being inflated at a constant rate of 25 cm^3/sec. At what rate in cm/sec is the radius of the ballon changing when the radius of the ballon is 2 cm? (VOLUME SPHERE FORMULA 4/3 pi r^3)

Answer 1

the surface area of the surface of the sphere, 4 pi r^2 times change in radius is the differential change in volume.

v = (4/3) pi r^3
dv/dt = 4 pi r^2 dr/dt


dr/dt = dv/dt /(4 pi r^2)