if the surface area of a sphere is given by the formula SA=4pir^2, find the rate of increase of the surface area if the radius is 4 cm and is increasing at the rate of 0.5 cm/min.

Answer 1

given: dr/dt = .5 cm/min
r = 4

SA = 4πr^2
d(SA)/dt = 8πr dr/dt
= 8π(4)(.5)
= 16π cm^2/min