Question

The surface area, S, of a sphere of radius r feet is S = S(r) = 4πr^2. Find the instantaneous rate of change of the surface area with respect to the radius r at r = 8.

Answer 1

This is the derivative of S with respect to r, evaluated at r=8.
dS/dr = 8πr
Substituting r=8 into the above gives the answer of 64π.