Mathematics

Problem

A right circular cylinder has a fixed volume of

500\text{ cm}^3

. As the cylinder is reshaped, its radius

r

increases at

0.20\text{ cm/s}

while the height adjusts so that the volume remains constant. The surface area of the cylinder is

S = 2\pi r h + 2\pi r^2

. Determine the value of

r

(in cm) at which the surface area is momentarily stationary (neither increasing nor decreasing). Express your answer in exact form.