Question

The surface area, S, of a sphere of radius r feet is S = S(r) = 4πr2. Find the instantaneous rate of change of the surface area with respect to the radius r at r = 4.
a. 32pi
b. 16pi
c. 64pi
d. 4pi

Answer 1

S = 4πr^2
Instantaneous rate of change = dS/dr = 8πr
At r = 4, Instantaneous rate of change = 8π(4) = 32π.