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

Instantaneous rate of change = S'(r) = 8πr
S'(8) = 8π(8) = 64π

Therefore, the instantaneoud rate of change of the surface area with respect to the radius r at r = 8  is 64π