Question

A balloon used in surgical procedures is cylindrical in shape. as it expands outward, assume that the length remains a constant . find the rate of change of surface area with respect to radius when the radius is (answer can be left in terms of π).

Answer 1

A cylinder's volume is π r² h, and its surface area is 2π r h + 2π r².  Since there is no length and radius. Let is denote the length by 80 mm and 0.30 mm radius.
Surface area, A = 2 (pi) r * 80 = 160(pi)r 
dA / dr = 160 (pi)
160.0π mm^2/mm is the answer.