Solve the Problem $40.0 \mathrm {~mm}$ Find the Rate of Change of Surface Area with Cylindrical

Multiple Choice

Solve the problem.
-A balloon used in surgical procedures is cylindrical in shape. As it expands outward, assume that the length remains a constant $40.0 \mathrm {~mm}$ . Find the rate of change of surface area with respect to radius when the radius is $0.080 \mathrm {~mm}$ . (Answer can be left in terms of $\pi$ ) .

A) $80.0 \pi \mathrm { mm } ^ { 2 } / \mathrm { mm }$
B) $40.32 \pi \mathrm { mm } ^ { 2 } / \mathrm { mm }$
C) $80.32 \pi \mathrm { mm } ^ { 2 } / \mathrm { mm }$
D) $40.16 \pi \mathrm { mm } ^ { 2 } / \mathrm { mm }$